Integrated control system for stability control of yaw, roll and lateral motion of a driving vehicle using an integrated sensing system with pitch information

ABSTRACT

An integrated stability control system using the signals from an integrated sensing system for an automotive vehicle includes a plurality of sensors sensing the dynamic conditions of the vehicle. The sensors include an IMU sensor cluster, a steering angle sensor, wheel speed sensors, any other sensors required by subsystem controls. The signals used in the integrated stability controls include the sensor signals; the roll and pitch attitudes of the vehicle body with respect to the average road surface; the road surface mu estimation; the desired sideslip angle and desired yaw rate from a four-wheel reference vehicle model; the actual vehicle body sideslip angle projected on the moving road plane; and the global attitudes. The demand yaw moment used to counteract the undesired vehicle lateral motions (under-steer or over-steer or excessive side sliding motion) are computed from the above-mentioned variables. The braking control is a slip control whose target slip ratios at selective wheels or wheel are directly generated from the request brake pressures computed from the demand yaw moment.

TECHNICAL FIELD

The present invention relates generally to a control apparatus forcontrolling a system of an automotive vehicle in response to senseddynamic behavior, and more specifically, to a method and apparatus fordynamically controlling a yaw, roll and lateral stability of a vehiclein response to the motion states of the vehicle measured and sensedthrough an integrated sensing system.

BACKGROUND

Various automotive vehicles have recently begun including vehicle systemcontrols. Vehicle system controls use the sensors to sense a vehicle'sdynamics, the driver's intention or even the environmental informationaround the vehicle; use the electronic control units (ECUs) to processthe sensed information; and use the available actuators to conductsuitable control actions requested from the ECUs so as to achievecontrolled performance for a driving vehicle. The ongoing goal of thevehicle system controls is to achieve an improved system performance ornew functions. Ultimately, the various vehicle control systems need tobe coordinately controlled so as to achieve enhanced system levelcontrol performances for ride, handling, safety and fuel economy of thevehicle.

One of the vehicle system controls are the various types of vehicledynamics controls, which use electronically controlled chassis,powertrain or drivetrain subsystems to augment the driver'scontrollability of the vehicle for ride, handling and safety purposes.

Several existing stability control systems are available. For example,the yaw stability control system (YSC) or a roll stability controlsystem (RSC) are currently equipped on millions of vehicles. Theseparated stability control functions are the focuses of the existingsystems.

It may be desirable to integrate the functions of the various dynamiccontrol systems. One reason that such an integration is desirable isthat there is overlap among the operation ranges of the individualcontrol systems. For example, a rollover control system tries to forcethe vehicle under-steer more during an un-tripped rollover event, whilean ESC system might take the vehicle's response under RSC control as anindication of the vehicle's true under-steer to conduct the vehicle'sunder-steer correction. If there is no integration between RSC and YSC,the control action of those may cancel each out. Hence a successfulimplementation of RSC and YSC in the same vehicle will need controlcoordination. One of the enablers of the coordination relies in theaccurate discrimination of the features of different unstable vehicledynamics, which require different control functions.

With current advances in mechatronics, the aforementioned technologyenabler is possible. For example, the advanced sensors might be used.Such advanced sensors together with other mechatronics not only helpfunction integration, they also helps improve the individual vehiclestability control performances and provides opportunities for achievingcontrol performances which were previously reserved for spacecraft andaircraft. For example, gyro sensors, previously only used in aircraftand spacecraft, have now been incorporated in various vehicle dynamicscontrols and the anti-lock brake systems once invented for airplanes arenow standard automotive commodities.

With the application of the advanced sensors and mechatronics, superiorinformation about the vehicle's dynamics states can be obtained whichcan be used to calculate effective feedback and feedforward controls forvarious functions and their integrations. It is especially effective touse the superior information from the advanced sensors and theirinnovative sensing algorithms to identify the scenarios, which areotherwise undetectable during a driving involved with complicated roadconditions and aggressive driving inputs from the driver.

A typical vehicle stability control and an integrated stability controlsystem sense and control a vehicle's dynamics conditions described inthe 3-dimensional space. Those control systems might require themeasurements of all or part of the three-dimensional motions whichinclude the rotational motions along the vehicle's roll, pitch, and yawdirections and the translation motion along the vehicle's longitudinal,lateral and vertical directions.

More specifically, in a typical vehicle stability control system such asa yaw stability control system or a roll stability control system, theprimary control task is to stabilize the vehicle in yaw or rolldirections, which will likely involve motions along its roll and yawdirections, and longitudinal and lateral directions. The couplingbetween different motion directions may not be as strong as in anaircraft or a spacecraft; however, they cannot be neglected in most ofthe control regions where unstable vehicle dynamics is seen. Unstablevehicle dynamics might involve rolling over or yawing out of thetraveling course during aggressive driving when the driver's inputs arewell beyond the values allowed by the adhesion limit of the roadsurface. For example, the excessive steering of a vehicle will likelylead to a unstable yaw and lateral motions, which further cause largerolling motion towards the outside of the turn. If the driver brakes thevehicle during such an excessive steering, the vehicle will also haveroll and pitch motions, large load transfer and large lateraldiscursion. It is desirable for a high performance stability controlsystem to integrate YSC, RSC and lateral stability control (LSC) suchthat the coupled unstable vehicle dynamics can be stabilized.

Theoretically, if there are sensors which can directly measure thevehicle's roll states, yaw states and lateral states during complicatedunstable dynamics, the successful integration would involve: (i)identifying the dominated direction where a primary unstable dynamicscan occur; (ii) prioritizing control functions when multiplesafety-critical unstable vehicle dynamics can occur; (iii) maximizingcontrol functions when multiple unstable vehicle dynamics are equallycritical; (iv) determining transition control actions from one stabilitycontrol function to another or to a normal operation function. Thedecision rule for any of the above actions needs close discrimination.Unfortunately, there are no direct measurements of the aforementionedvehicle states. Even the advanced sensors can only provide indirectmeasurements of the involved vehicle states. Therefore, intelligentsensing algorithms are required.

Therefore, it would be desirable to integrate the YSC, RSC and LSCfunctions to provide accurate determination of the involved roll, yawand lateral motions of a vehicle. The controllable variables associatedwith those motions might be the vehicle's global and relative angularmotion variables such as attitudes and the directional motion variablessuch as the longitudinal and lateral velocities. For instance, in RSC,the relative roll angle between the vehicle body and the road surface iscontrolled. In LSC, the relative yaw angle between the vehicle's traveldirection and the path is controlled. The coupled dynamics among roll,yaw and pitch motions and the elevated (banked or inclined) road causedvehicle motions all need to be differentiated. The driver'sintention-based vehicle dynamic behavior will also need to bedetermined. Due to the fact that the sensors measure the total motion ofthe vehicle, the sensor measurements contain the total information thatincludes the values of the driver-induced dynamics, the roadgeometry-induced dynamics and the dynamics from the gravity togetherwith sensor uncertainties. It is not hard to find that separating thedriver-induced dynamics and the road-induced dynamics from the totalsensor measurements need intelligent algorithms. Only if suchinformation is determined from the total sensor measurements, thecontrol system can provide adequate control actions in needed situations(driver-induced excessively dynamic or unstable) and generate lessoccurrences of false control action in unneeded situations such as incertain road geometry-induced dynamics.

In order to achieve the aforementioned separation of the drivermaneuver-induced vehicle dynamics information and the roadgeometry-induced dynamics information from the sensor uncertainties,gravity-induced dynamics terms, a new vehicle sensing technology whichcontains an inertial measurement unit (IMU) has been pursued at FordMotor Company. This sensing system is called an Integrated SensingSystem (short to ISS) in this invention.

The IMU has been used in inertial navigation system (INS) for aircraft,spacecraft and satellite for decades. Typically an INS system determinesthe attitude and directional velocity of a flight vehicle through thesensor signals from the IMU sensors and GPS signals. The IMU sensor setincludes 3 gyros and 3 linear accelerometers. The INS contains an IMUand a processor unit to compute the navigation solutions necessary fornavigation, attitude reference and various other data communicationsources. As the same token, the ISS will also be used (but not limited)to determine the vehicle's attitude and directional velocities with theexception that GPS signals are not necessarily used but, instead, theother sensor signals such as ABS wheel speed sensor signals are used.

With the availability of the IMU sensor cluster equipped with a vehiclestability control system, several effects which are impossible todifferentiate in the traditional stability control may now be included.For example, the effect of the road bank was not accurately included inthe existing control algorithm. Many known systems either rely uponbasic assumptions regarding conditions such as driving on a flat surface(no pitch or bank angle) or on an estimated road bank information thatis usually accurate in non-event situation (e.g., steady state driving)but inaccurate in vehicle stability control events. Due to the use ofIMU sensor cluster in the ISS system, the road bank and gradeinformation may now be fairly accurately determined.

Notice that the vehicle's attitudes are required to separate the gravitycontamination in the acceleration sensor signals. This can be seen fromthe following example. The vehicle's lateral sliding used in LSC can becharacterized by its lateral velocity defined along the lateraldirection of the vehicle body. Such a velocity cannot be directlymeasured and it is determined from the lateral accelerometermeasurement. The total output of the lateral accelerometer containsinformation that is related to the variables other than the lateralvelocity. This information includes gravity contamination, thecentripetal accelerations, the derivative of the lateral velocity, thesensor uncertainties. On a banked road, the gravity contributes to thelateral accelerometer measurement as significantly as the combination ofthe vehicle's true lateral velocity derivative and the centripetalacceleration. Due to the fact that the gravity is fixed in both itsmagnitude and its direction with respect to the sea level, the vehicleglobal attitudes can be used to find the relative position between thegravity vector and the vehicle's body directions. For this reason, thevehicle global attitudes can be used to compensate the gravity influencein the measured lateral acceleration such that the vehicle lateralvelocity might be isolated and determined from the lateral accelerationsensor measurement. The same argument would hold for using pitchattitude to compensate the longitudinal accelerometer sensor signals forcomputing the vehicle's longitudinal velocity.

While driving on a level ground, the vehicle lateral acceleration tendsto be larger than the value sustained by the limits of adhesion on a drysurface with high adhesion due to the large load transfer. On a slipperysurface with low adhesion, the vehicle's lateral acceleration might beclose to the limit of adhesion of the road surface. The accelerationsensors used in the existing YSC system could not provide information todifferentiate this especially when a vehicle experiences large roll andpitch accelerations in excessive maneuvers. Due to the relative attitudedetermination from the RAD unit in the ISS system, such load transfereffects may be easily characterized. Therefore a stability controlsystem using ISS system output would be able to achieve the same physicsin the low adhesion road surface with in the high adhesion road surface,and less deviation of control performance in low adhesion road from thecontrol performance in the high adhesion road will be experienced.

It is the objective of the current disclosure to provide an integratedsensing system and use such information for an integrated stabilitycontrol system to coordinate a yaw stability control function, rollstability control function and a lateral stability control function toachieve superior control performance in comparison with the existingvehicle stability control systems.

SUMMARY

The present invention's focus is on the type of vehicle dynamic controlsystems that control the multiple motions of the vehicle along yaw, rolland lateral directions during the driver initiated maneuvers Themultiple motions are likely to be unstable if their controls are onlyconducted by an ordinary driver. For this reason, such vehicle dynamicscontrols are also called the vehicle stability control systems.

One theme of this invention is an integrated treatment of the potentialvehicle stability controls through superior vehicle's operation statedetermination using an integrated sensing system. That is, an integratedstability control system (ISCS) is used to stabilize individual ormultiple unstable vehicle dynamics at the same time. More specifically,integration of yaw, roll and lateral stability control systems isdesirable.

The present invention provides an integrated sensing system (ISS) anduses the information from such a sensing system to conduct integratedstability control system which integrates a yaw stability control system(YSC), a roll stability control (RSC) system and a lateral stabilitycontrol (LSC) system together with an anti-brake-lock system (ABS), atraction control system (TCS). The integrated sensing system usessignals measured from the sensor set beyond the sensor configurationused in the traditional YSC, RSC, ABS and TCS systems. The sensors usedin the ISS include a six-degree of freedom inertial measurement unit(IMU), a steering wheel angle (SWA) sensor, four ABS wheel speedsensors, a master cylinder brake pressure sensor, a brake pedal forcesensor, and other sensors. The powertrain and drivetrain information andthe other available information are also fed into the ISS.

Notice that the traditional ESC system integrates ABS, TCS and yawstability management functions through individual brake pressurecontrols (incremental to the driver requested brake pressures). The maingoal of an ESC is to augment the driver's controllability of the vehicleat the limit of the vehicle dynamics for a given road surface tractionand for a given set of the driver requested driving inputs. Thecontrollability of ESC mainly focuses on the vehicle's yaw rate responsewith respect to the driver's intension (determined from the inputs suchas the driver's steering wheel angle input, the vehicle speed, and thelike).

Although various ESC systems claim to have certain lateral stabilitycontrol, its effectiveness is limited due to the fact that the sensorset used in ESC cannot accurately and robustly differentiate the effectof the road bank and the vehicle's lateral instability. If the vehicleis stable in lateral direction, the bank effect may be determined. Butwhen the vehicle is driving close to lateral instability on amedium-sized bank road, it may not be possible to separate the vehicle'slateral siding motion from the bank influence (gravity contamination) inthe lateral acceleration sensor measurement. This is especially the casewhen the vehicle is driven on low friction road surfaces.

The vehicle's lateral sliding usually increases the vehicle dynamicallyunstable tendency such that the vehicle is hard to control by ordinarydrivers. Hence one of the performance requirements in vehicle stabilitycontrols is to attenuate the lateral sliding as much as possible. Noticethat such a performance requirement is different from car racing, wherevehicle lateral sliding is sacrificed for vehicle driving speed. Onereason is that racecar drivers are usually capable and experienceddrivers, who can handle the vehicle well even if it is experiencinglarge lateral sliding. The vehicle's lateral sliding used in LSC can becharacterized by its lateral velocity defined along the lateraldirection of the vehicle body. Such a velocity cannot be directlymeasured and is determined from the lateral accelerometer measurement.The total output of the lateral accelerometer contains information thatis related to the variables other than the lateral velocity. Thisinformation includes gravity contamination, the centripetalaccelerations, the derivative of the lateral velocity, and the sensoruncertainties. On a banked road, the gravity contributes to the lateralaccelerometer measurement as significantly as the combination of thevehicle's true lateral velocity derivative and the centripetalacceleration. Due to the fact that gravity is fixed in both magnitudeand direction with respect to the sea level, the vehicle globalattitudes may be used to find the relative position between the gravityvector and the vehicle's body directions. For this reason, the vehicleglobal attitudes can be used to compensate the gravity influence in themeasured lateral acceleration such that the vehicle lateral velocitymight be isolated and determined from the lateral acceleration sensormeasurement. The same argument would hold for using pitch attitude tocompensate the longitudinal accelerometer sensor signals for computingthe vehicle's longitudinal velocity.

Sideslip angle is the inverse tangent of the ratio of the lateralvelocity and the longitudinal velocity of the vehicle defined on thevehicle's body fixed coordinate system. Therefore, its accuratedetermination must involve the accurate determination of thelongitudinal and lateral velocities of the vehicle defined on thevehicle's body-fixed coordinate system.

In one aspect, an improvement is realized by using additional sensorssuch as a pitch rate sensor and/or a vertical acceleration sensor in thevarious determinations. One advantage of the invention is that in thenear term such sensors may be included in a single module such as in aninertial measurement unit (IMU) that is frequently used in aircraft andspacecraft Therefore, improvements to sensing technology may be realizedwithout additional or with minimal cost.

In another aspect of the invention, a method of controlling a vehicleincludes determining a yaw rate from a yaw rate sensor, determining apitch rate from a pitch rate sensor, determining a lateral accelerationfrom a lateral acceleration sensor, determining a vehicle speed from avehicle speed sensor and the other signals, and controlling anintegrated stability control system in response to the yaw rate, pitchrate, lateral acceleration, and vehicle speed.

Of course, various other sensors such as a roll rate sensor, steeringangle sensor, longitudinal acceleration sensors and a verticalacceleration signal may be combined together or independently with theabove-mentioned sensors to further refine control of the system.

In a further aspect of the invention, a method of controlling a vehiclecomprises determining the outputs from an integrated sensing system,using those outputs to conduct vehicle stability controls.

In a further aspect of the invention, a method of controlling a vehiclecomprises integrating YSC, RSC and LSC through the output signalscalculated in the integrated sensing system.

Other advantages and features of the present invention will becomeapparent when viewed in light of the detailed description of thepreferred embodiment when taken in conjunction with the attacheddrawings and appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic view of a vehicle with variable vectors andcoordinate frames according to the present invention.

FIG. 2 is a block diagram of a stability system according to the presentinvention.

FIG. 3 is a front view of an automotive vehicle illustrating variousangles according to the present invention.

FIG. 4 is a side view of an automotive vehicle illustrating variousvariables thereon.

FIG. 5 is a top view of a vehicle according to the present invention.

FIG. 6 is a detailed block diagrammatic view of a controller accordingto the present invention.

FIG. 7 is a flow chart illustrating a method of controlling the vehicleaccording to the present invention.

FIG. 8 is another method for determining the lateral velocity of thevehicle.

FIG. 9 is a block diagrammatic view of a longitudinal velocityestimation block

FIG. 10 is a more detailed block diagrammatic view of a method fordetermining longitudinal velocity.

FIG. 11 is a flow chart illustrating a method for determining thelongitudinal velocity of the vehicle.

FIGS. 12A, 12B and 12C illustrate a vehicle without stability control, avehicle with traditional stability control, and a vehicle with advancedstability control according to the present invention, respectively.

DESCRIPTION OF THE PREFERRED EMBODIMENT

In the following figures the same reference numerals will be used toidentify the same components. The present invention is preferably usedin conjunction with vehicle control systems including but are notlimited to a yaw stability control (YSC) system, a roll stabilitycontrol (RSC) system, a lateral stability control (LSC), an integratedstability control system (ISCS), or a total vehicle control system forachieving fuel economy and safety and other vehicle level performances.The system is also described with respect to an integrated sensingsystem (ISS) which uses a centralized motion sensor cluster such as aninertial measurement unit (IMU) and the other available butdecentralized sensors. Although the centralized motion sensor such as anIMU is used, the methods described here are easily transferable to usingthe other discrete sensors.

Referring to FIG. 1, an automotive vehicle 10 with a vehicle dynamicscontrol or an active safety system of the present invention isillustrated with the various forces and moments thereon during a stablevehicle dynamic condition. Vehicle 10 has front right (FR) and frontleft (FL) wheel/tires 12A and 12B and rear right (RR) wheel/tires 13Aand rear left (RL) wheel/tires 13B, respectively. The vehicle 10 mayalso have a number of different types of front steering systems 14 a andrear steering systems 14 b, including having each of the front and rearwheels configured with a respective controllable actuator, the front andrear wheels having a conventional type system in which both of the frontwheels are controlled together and both of the rear wheels arecontrolled together, a system having conventional front steering andindependently controllable rear steering for each of the wheels, or viceversa. Generally, the vehicle has a weight represented as Mg at thecenter of gravity of the vehicle, where g=9.8 m/s² and M is the totalmass of the vehicle.

As mentioned above, the system may also be used with the other vehicledynamics controls such as ride and handling control systems includingactive/semi-active suspension systems, anti-roll bar, or the othersafety systems such as airbags or passive safety devices deployed oractivated upon sensing predetermined dynamic conditions of the vehicle.

The ISS unit 16 is coupled to the ISCS unit 18. The ISS unit 16 maycomprise many different sensors as will be described further below. Thesensors may also be used by the ISCS unit in various determinations suchas to determine a wheel lifting event such as in an imminent rollover,determine various forces including normal forces at the wheels,determine a height and position of a mass, determine the instabilitytrend of the unstable dynamics as in unstable roll or yaw motions,determine the driver's intention, determine the feedforward controlcommands to drive actuators, determine feedback control commands for thedesired functions, and the like. The wheel speed sensors 20 are mountedat each corner of the vehicle and generate signals corresponding to therotational speed of each wheel which are denoted as w₁, w₂, w₃, w₄ orw_(slf), w_(srf), w_(slr), w_(srr) for left-front, right-front,left-rear and right-rear wheels, respectively. The rest of the sensorsused in ISS unit 16 may include the other decentralized sensors and acentralized motion sensor such as an IMU or a RSC sensor cluster mounteddirectly on a rigid surface of the vehicle body such as the vehiclefloor or the chassis frame. The centralized sensor cluster may notdirectly measure the motion variables along the vehicle body fixedlongitudinal, lateral or vertical directions, it only provide motionvariable information of the vehicle body at the sensor location andalong the sensor's local directions.

As those skilled in the art will recognize, the frame from b₁, b₂ and b₃is called a body frame 22, whose origin is located at the center ofgravity of the car body, with the b₁ corresponding to the x axispointing forward, b₂ corresponding to the y axis pointing off thedriving side (to the left), and the b₃ corresponding to the z axispointing upward. The angular rates of the car body are denoted abouttheir respective axes as ω_(bx) for the roll rate, ω_(by) for the pitchrate and ω_(bz) for the yaw rate. Calculations may take place in aninertial frame 24 that may be derived from the body frame 22 asdescribed below. The longitudinal acceleration of the vehicle body isdenoted as a_(bx). The lateral acceleration of the vehicle body isdenoted as a_(by). The vertical acceleration of the vehicle body isdenoted as a_(bz).

As mentioned before, the centralized motion sensor might have differentdirections than the vehicle body-fixed directions. Such a centralizedsensor cluster might be mounted on a specific location of the vehiclebody. The frame system s₁s₂s₃ fixed on the sensor cluster body is calleda sensor frame system. The sensor frame directions are denoted as s₁, s₂and s₃ which are the x-y-z axes of the sensor frame. Notice that thesensor frame system is not necessary the same as the vehicle body fixedframe system b₁b₂b₃. One of the reasons is that the sensor mountingerrors are possible in the production environment. For practicalreasons, the centralized sensor cluster like an IMU may not be mountedon the same location which is of interest for computation purposes suchas the vehicle's center of gravity or the rear axle of the vehicle body.However, it is evident that an IMU sensor measures enough information tobe used to numerically translate the IMU sensor output to the motionvariables at any location on the vehicle body. The six outputs of theIMU sensor along its sensor frame are denoted as ω_(sx), ω_(sy), ω_(sz),a_(sx), a_(sy) and a_(sz) for the sensor cluster's roll rate, pitchrate, yaw rate, longitudinal acceleration, lateral acceleration andvertical acceleration.

The other frame used in the following discussion includes the movingroad frame, as depicted in FIG. 1. The moving road frame system r₁r₂r₃is fixed on the driven road surface, where the r₃ axis is along theaverage road normal direction of a plane called a moving road plane. Themoving road plane is a flat plane, which serves as an averagerepresentation of the four-tire/road contact patches and it is usually afictitious plane. If the road surface is perfectly flat, then itcoincides with the moving road surface. Let the four verticalcoordinates of the centers of the contact patches with respect to theinertia frame or sea level be z₀, z₁, z₂, z₃ for the front-left,front-right, rear-left and rear-right corners, then the average movingroad plane experienced by the driven vehicle should have the bank anglecomputed as

$\begin{matrix}{{{average}\mspace{14mu}{road}\mspace{14mu}{bank}} = {\frac{1}{4}\left( {\frac{z_{0} - z_{1}}{t_{f}} + \frac{z_{2} - z_{3}}{t_{r}}} \right)}} & (1)\end{matrix}$where t_(f) and t_(r) are the half tracks of the front and rear axles,and the inclination angle computed as

$\begin{matrix}{{{average}\mspace{14mu}{road}\mspace{14mu}{slope}} = {\frac{1}{2}\left( {\frac{z_{2} - z_{0}}{b} + \frac{z_{3} - z_{1}}{b}} \right)}} & (2)\end{matrix}$where b is the wheel base of the vehicle.

Notice that the moving road plane is moving and yawing with the vehiclebody but it is not rolling and pitching with the vehicle body. Themoving road frame is the right-hand orthogonal axis system r₁r₂r₃ inwhich the plane containing r₁ and r₂ axes coincides with the averagemoving road plane. That is, r₁-axis is the projection of thelongitudinal axis of the vehicle body on to the average moving roadplane, r₂-axis is the projection of the lateral axis of the vehicle bodyon to the average moving road plane, and r₃-axis points upwards whichcoincides with the normal direction of the average moving road plane.Notice that the moving road frame coincides with an ISO-8855'sintermediate axis system if the vehicle is driven on a level ground. Ona three-dimensional road, there is no counterpart defined in ISO-8855.

Referring now to FIG. 2, the ICSC unit 18 is illustrated in furtherdetail having an ISS unit 26 used for receiving information from anumber of sensors which may include a yaw rate sensor 28, a speed sensor20, a lateral acceleration sensor 32, a vertical acceleration sensor 33,a roll angular rate sensor 34, a hand wheel sensor 35 (steering wheelwithin the vehicle), a longitudinal acceleration sensor 36, a pitch ratesensor 37, steering angle (of the wheels or actuator) position sensor 38(steered wheel angle), a suspension position (height) sensor 40. Itshould be noted that various combinations and sub-combinations of thesensors may be used.

The sensor cluster 16 may be disposed within a single housing 43, andincludes a roll rate sensor 34 generating a roll rate signal, a pitchrate sensor 37 generating a pitch rate signal, a yaw rate sensor 38generating a yaw rate signal, a longitudinal acceleration sensor 36generating a longitudinal acceleration signal, a lateral accelerationsensor 32 generating a lateral acceleration signal, and a verticalacceleration sensor 33 generating a vertical acceleration.

In typical aerospace application, the centralized motion sensor like IMUis always used together with global positioning system (GPS) signals.Recently, such an approach has also made into automotive applications,see for example, “Integrating INS sensors with GPS velocity measurementsfor continuous estimation of vehicle sideslip and tire corneringstiffness” by D. M. Bevly, R. Sheridan and J. C. Gerdes in proceeding ofthe 2001 American Control Conference. In the present invention, GPS isnot required.

Based upon inputs from the sensors, the ISS unit 26 may feed informationto the ISCS unit 44 that further drives the actions of the availableactuators. Depending on the desired sensitivity of the system andvarious other factors, not all the sensors may be used in a commercialembodiment. The ISCS unit 44 may control an airbag 45 or a steeringactuator 46A-46D at one or more of the wheels 12A, 12B, 13A, 13B of thevehicle. Also, other vehicle subsystems such as a suspension control 48may be used for ride, handling and stability purpose.

Roll angular rate sensor 34 and pitch rate sensor 37 may be replaced bysensors sensing the height of one or more points on the vehicle relativeto the road surface to sense the roll condition or lifting of thevehicle. Sensors that may be used to achieve this include but are notlimited to a radar-based proximity sensor, a laser-based proximitysensor and a sonar-based proximity sensor. The roll rate sensor 34 mayalso be replaced by a combination of sensors such as proximity sensorsto make a roll determination.

Roll rate sensor 34 and pitch rate sensor 37 may also be replaced bysensors sensing the linear or rotational relative displacement ordisplacement velocity of one or more of the suspension chassiscomponents to sense the roll condition or lifting of the vehicle. Thismay be in addition to or in combination with suspension distance sensor40. The suspension distance sensor 40 may be a linear height or travelsensor and a rotary height or travel sensor.

The yaw rate sensor 28, the roll rate sensor 34, the lateralacceleration sensor 32, and the longitudinal acceleration sensor 36 maybe used together to determine that single wheel or two wheels of avehicle are lifted and the quantitative information regarding therelative roll information between the vehicle body and moving road planesuch as in RSC developed at Ford. Such sensors may also be used todetermine normal loading associated with wheel lift.

The roll condition such as the relative roll angle of the vehicle bodywith respect to the road surface or with respect to the sea level mayalso be established by one or more of the following translational orrotational positions, velocities or accelerations of the vehicleincluding the roll rate sensor 34, the yaw rate sensor 28, the lateralacceleration sensor 32, the vertical acceleration sensor 33, a vehiclelongitudinal acceleration sensor 36, lateral or vertical speed sensorincluding a wheel-based speed sensor 20, a radar-based speed sensor, asonar-based speed sensor, a laser-based speed sensor or an optical-basedspeed sensor.

The ISS unit 26 may include sensing algorithms including but not limitedto reference attitude and reference directional velocity determinations,global/relative attitude determination, directional velocitydetermination, sensor plausibility check, sensor signal conditioning,road parameter determination, and abnormal state monitoring.

The ISS unit 26 includes various control units controlling theaforementioned sensing algorithms. More specifically, these units mayinclude: a reference signal unit 70 (reference signal generator (RSG)),which includes an attitude reference computation and a velocityreference computation, a road profile unit 72 (road profiledetermination unit (RPD)), an attitude unit or relative attitudedetermination unit 74 (RAD), a global attitude unit 76 (global attitudedetermination unit (GAD) and a directional velocity unit 78 (directionalvelocity determination unit (DVD)), a sensor plausibility unit 80(sensor plausibility check unit (SPC)), an abnormal state unit 82(abnormal state monitoring unit (ASM)), a sensor signal compensatingunit 84 (SSC), an estimation unit 86 (force and torque estimation unit(FATE)), a car body to fixed reference frame unit 88 (body to referenceunit (B2R)), a normal loading unit 90 (normal loading determination unit(NLD)), a vehicle parameter unit 92 (vehicle parameter determinationunit (VPD)), a four wheel driver reference model 94 and a sideslip anglecomputation 96. Signals generated from any one of the aforementionedunits are referred to prediction of vehicle operation states signals.

The ISCS unit 44 may control the position of the front right wheelactuator 46A, the front left wheel actuator 46B, the rear left wheelactuator 46C, and the right rear wheel actuator 46D. Although asdescribed above, two or more of the actuators may be simultaneouslycontrolled. For example, in a rack-and-pinion system, the two wheelscoupled thereto are simultaneously controlled. Based on the inputs fromsensors 28 through 43B, controller 26 determines a roll condition and/orwheel lift and controls the steering position and/or braking of thewheels.

The ISCS unit 44 may be coupled to a brake controller 60. Brakecontroller 60 controls the amount of brake torque at a front right brake62 a, front left brake 62 b, rear left brake 62 c and a rear right brake62 d. The functions performed through ISCS might include an RSC function110, a YSC function 66, and an LSC function 69. The other functionalunits such as an antilock-braking system (ABS) unit 64 and a tractioncontrol system (TCS) unit 65 may be provided by the brake suppliers andare usually controlled through signals calculated from the supplier'ssensing and control module (which might uses the same or part of thesensors used in this invention). Those functions might be improvedthrough utilizing the signals calculated in ISS unit.

Speed sensor 20 may be one of a variety of speed sensors known to thoseskilled in the art. For example, a suitable speed sensor may include asensor at every wheel that is averaged by the SS unit 26. The algorithmsused in ISS may translate the wheel speeds into the travel speed of thevehicle Yaw rate, steering angle, wheel speed, and possibly a slip angleestimate at each wheel may be translated back to the speed of thevehicle at the center of gravity. Various other algorithms are known tothose skilled in the art. Speed may also be obtained from a transmissionsensor. For example, if speed is determined while speeding up or brakingaround a corner, the lowest or highest wheel speed may not be usedbecause of its error. Also, a transmission sensor may be used todetermine vehicle speed instead of using wheel speed sensors.

Although the above discussions are valid for general stability controls,some specific considerations of using them in RSC will be discussed. Theroll condition of a vehicle during an imminent rollover may becharacterized by the relative roll angle between the vehicle body andthe wheel axle and the wheel departure angle (between the wheel axle andthe average road surface). Both the relative roll angle and the wheeldeparture angle may be calculated in relative roll angle estimationmodule (RAD 74) by using the roll rate, lateral acceleration sensorsignals and the other available sensor signals used in ISS unit. If boththe relative roll angle and the wheel departure angles are large enough,the vehicle may be in either single wheel lifting or double wheellifting. On the other hand, if the magnitude of both angles is smallenough, the wheels are likely all grounded; therefore the vehicle is notrolling over. In case that both of them are not small and the doublewheel lifting condition is detected or determined (see for example U.S.Pat. No. 6,904,350), the sum of those two angles will be used to computethe feedback commands for the desired actuators so as to achieverollover prevention. The variables used for this purpose might beincluded in the ISS unit.

The roll information of a vehicle during an imminent rollover may becharacterized by rolling radius-based wheel departure roll angle, whichcaptures the angle between the wheel axle and the average road surfacethrough the dynamic rolling radii of the left and right wheels when bothof the wheels are grounded. Since the computation of the rolling radiusis related to the wheel speed and the linear velocity of the wheel, suchrolling-radius based wheel departure angle will assume abnormal valueswhen there are large wheel slips. This happens when a wheel is liftedand there is torque applied to the wheel. Therefore, if this rollingradius-based wheel departure angle is increasing rapidly, the vehiclemight have lifted wheels. Small magnitude of this angle indicates thewheels are all grounded. The variables used for this purpose might beincluded in the ISS unit.

The roll condition of the vehicle during an imminent rollover may beseen indirectly from the wheel longitudinal slip. If during a normalbraking or driving torque the wheels at one side of the vehicleexperience increased magnitude of slip, then the wheels of that side arelosing longitudinal road torque. This implies that the wheels are eitherdriven on a low mu surface or lifted up. The low mu surface conditionand wheel-lifted-up condition may be further differentiated based on thechassis roll angle computation, i.e., in low mu surface, the chassisroll angle is usually very small. The variables used for this purposemight be included in the ISS unit.

The roll condition of the vehicle during an imminent rollover may becharacterized by the normal loading sustained at each wheel.Theoretically, when a normal loading at a wheel decreases to zero, thewheel is no longer contacting the road surface. In this case a potentialrollover is underway. Large magnitude of this loading indicates that thewheel is grounded. Normal loading is a function of the calculatedchassis roll and pitch angles. The variables used for this purpose mightbe included in the ISS unit.

The roll condition of a vehicle during imminent rollover may beidentified by checking the actual road torques applied to the wheels andthe road torques, which are needed to sustain the wheels when they aregrounded. The actual road torques may be obtained through torquebalancing for each wheel using wheel acceleration, driving torque andbraking torque. If the wheel is contacting the road surface, thecalculated actual road torques must match or be larger than the torquesdetermined from the nonlinear torques calculated from the normal loadingand the longitudinal slip at each wheel. The variables used for thispurpose might be included in the ISS unit.

The roll condition of a vehicle during an imminent rollover may becharacterized by the chassis roll angle itself, i.e., the relative rollangle between the vehicle body and the wheel axle. If this chassis rollangle is increasing rapidly, the vehicle might be on the edge of wheellifting or rollover. Small magnitude of this angle indicates the wheelsare not lifted or are all grounded. Therefore, an accurate determinationof the chassis roll angle is beneficial for determining if the vehicleis in non-rollover events and such computation is conducted in RAD unitin ISS.

The roll condition of a vehicle during imminent rollover may also becharacterized by the roll angle between the wheel axle and the averageroad surface, which is called a wheel departure angle (WDA). If the rollangle is increasing rapidly, the vehicle has lifted wheel or wheels andaggressive control action needs to be taken in order to prevent thevehicle from rolling over. Small magnitude of this angle indicates thewheels are not lifted. The variables used for this purpose might beincluded in the ISS unit.

The ISCS unit 18 may include control function logic and control functionpriority logic. As illustrated, the logic resides within ISCS unit 44,but may be part of the ISS unit 26 and/or brake controller 60.

Referring now to FIG. 3, the relationship of the various angles of thevehicle 10 (end view of which is shown) relative to the road surface 11is illustrated. In the following, a reference road bank angle θ_(bank)is shown relative to the vehicle 10 on a road surface, The vehicle has avehicle body 10 a and wheel axle 10 b. The wheel departure angle θ_(wda)is the angle between the wheel axle and the road. The relative rollangle θ_(xr) is the angle between the wheel axle 10 b and the body 10 a.The global roll angle θ_(x) is the angle between the horizontal plane(e.g., at sea level) and the vehicle body 10 a.

Another angle of importance is the linear bank angle. The linear bankangle is a bank angle that is calculated more frequently (perhaps inevery loop) by subtracting the relative roll angle generated from alinear roll dynamics of a vehicle (see U.S. Pat. No. 6,556,908 which isincorporated by reference herein), from the calculated global roll angle(as one in U.S. Pat. No. 6,631,317 which is incorporated by referenceherein). If all things were slowly changing without drifts, errors orthe like, the linear bank angle and reference road bank angle termswould be equivalent.

During an event causing the vehicle to roll, the vehicle body is subjectto a roll moment due to the coupling of the lateral tire force and thelateral acceleration applied to the center of gravity of vehicle body.This roll moment causes suspension height variation, which in turnresults in a vehicle relative roll angle (also called chassis roll angleor suspension roll angle). The relative roll angle is used as an inputto the activation criteria and to construct the feedback brake pressurecommand for RSC function, since it captures the relative roll betweenthe vehicle body and the axle. The sum of such a chassis roll angle andthe roll angle between wheel axle and the road surface (called wheeldeparture angle) provides the roll angle between the vehicle body andthe average road surface, which is feeding back to the RSC module.

Referring now to FIGS. 4 and 5, an automotive vehicle 10 is illustratedwith various parameters illustrated thereon. The side view of automotivevehicle 10 is illustrated. A front suspension 82 and a rear suspension82 r are illustrated. The suspensions are coupled to the body at arespective suspension point 84 f, 84 r. The distance from the suspensionpoint 84 f to the center of the wheel is labeled z_(sh). The distancefrom the center of gravity CG to the front suspension is labeled asb_(f). The distance from the CG to the rear suspension point 84 r islabeled as b_(r). The vertical distance between the center of gravityand the suspension point are labeled respectively as h_(f) and h_(r). Aportion of the body axis b₃ and the road axis r₃ are illustrated. Theangle therebetween is the relative pitch angle θ_(yr). The rollingradius of the tire is labeled as z_(w).

Referring specifically now to FIG. 5, a top view of vehicle 10. Lateraland longitudinal velocities of the center of gravity are denoted asν_(x) and ν_(y), a yaw angular rate is denoted as ω_(z), a front wheelsteering angle is denoted as δ_(s), lateral acceleration is representedby a_(y), and longitudinal acceleration is represented by a_(x). Alsoillustrated is the front track width t_(f) and rear track width t_(r).That is, the track widths are half the track widths from the center lineor center of gravity of the vehicle to the center of the tire. Rear axle14 b extends between the rear wheels 13 a, 13 b. Various calculationsmay be performed relative to the rear axles of 14 b.

Referring now to FIG. 6, the interrelationship among the various unitsin a controlled vehicle dynamics is shown. The vehicle dynamics isrepresented by the module 102. The vehicle dynamics includes the angularand translation movements of the vehicle. The motion and actuationsensors 28-40 generate signals corresponding to the vehicle dynamics andthe actions of the various actuators. The sensors are fed into the ISSunit 104. The sensor signals and the calculated signals from a systemother than ISS (for example, the brake supplier's own brake controlcomputations) 106 may be fed into to sensing module 108. The ISS unit iscoupled to the ISCS unit 44 and may specifically be coupled to but notlimited to the RSC function module 110 and a YSC function module 66. Afunction priority system command 80 may also be included. The output ofthe TCS module 68 and the ABS module 64 may be coupled to priority logicsystem command 114, which in turn is coupled to the actuationdistribution and commanding block 116. The actuation distributioncommanding block 116 is coupled to the powertrain control ECU 118 and tothe brakes 119. The powertrain control module 118 may be coupled to theengine 120 and transmission 122. The actuation of the engine, the brakesand the transmission may affect the vehicle dynamics 102, which in turnis sensed by the various sensors. Thus, as can be seen, a continuousloop of sensing and controlling with respect to the vehicle dynamics isillustrated.

Referring now to FIG. 7, further detail of the operation ISS unit 26 isillustrated. The various computations in the SS unit begin in start step300. In step 302, signals from the various sensors are received. Thesensor electronics usually provide an indication of the quality of thesensor signal sent out from a specific sensor and the environmentaltemperature around the sensors may also be provided. Built-in self-testof the sensors may also be conducted through the sensor electronics. Instep 302, the signals from various sensors and sensor electronics arereceived. In this step, some extra actions other than “receiving” may beconducted. For example, the sensor signals are monitored for electricfailures that may include communication failures, wiring failures andpower supply failures. The communication failures may be due to adefective CAN hardware device, high frequency interference, CAN bus offevents, missing CAN message from the sensor electronics, too high CANload, wrong CAN controller configuration, and the like. The wiringfailures might be due to interruptions, short circuit, electronicsinterference and leakage. The power supply failures might be due toshort circuit to ground or to the wrong voltage, low voltage of thepower supply. The sensor signals are also monitored for sudden changesand for out-of range monitoring. A sudden signal change with very highchange rate might be a good indication of electronic failure of thesensor.

In step 304, the plausibility of the sensors is determined in the sensorplausibility check module (SPC). The main focus of SPC is on sensordefects, mechanical failures, or an implausible operation content. Forexample, a loose sensor might have certain implausible sensor(vibration) content which does not match the vehicle's motion; a sensormight be mounted incorrectly on the vehicle; the sensor electronics isgradually degraded (e.g., electronics component aging, electronic wiringaging) that cannot be detected through electronic monitoring). In allthese cases, the overall vehicle dynamics behavior is checked todetermine if certain sensor signals are plausible. For example, a rollrate plausibility check is conducted by comparing the roll rate sensorvalue with an roll rate estimation based on sensor signals other thanroll rate such as the lateral acceleration, the yaw rate, the wheelspeed and the steering wheel signals; a yaw rate plausibility check isconducted by comparing the yaw rate sensor value with an estimated yawrate value based on the steering wheel angle, the lateral accelerationand wheel speed signals.

In step 306, if at least one sensor is not plausible, step 308 isexecuted in which sensor fault processing logic is performed. Theplausibility flags are set and saved in an accessible memory. A reducedmodel computation will be conducted and a partial function control willbe determined. The info from the sensor fault processing logic will befed to the ISCS unit 44 through the signal flow 309.

In step 310, sensor signals are compensated in the sensor signalcompensation unit SSC. SSC will conduct sensor zero-point offsetcompensation, sensor signal drift (for example, due to ambienttemperature change) compensation), the sensor noise compensation, etc.The sensor mounting error such as sensor misalignments (see U.S. Pat.No. 6,782,315) might also be computed at this module.

In step 312, the abnormal operation states of the vehicle subsystems aremonitored in the abnormal state monitoring module ASM. The abnormalstates of the vehicle might be a flat tire or a tire with significantinflation pressure drop, a significant loading bias (such as a fulltrunk loading in a truck or a large roof loading in a SUV), off-shelfwheels, extreme wear of the brake pads, the imbalanced wheel (see U.S.Pat. No. 6,834,222). In step 313, if there are abnormal statespresented, the abnormal state processing unit is conducted in step 314.The abnormal state processing logic involves assessing the severity ofthe abnormal states in terms of influence of the ISCS functions. If theabnormal operation states are not critical, then certain compensationsof the involved signals will be compensated and the control function inISCS will be continued. For example, if ASM detects one of the tires hasa large tire pressure drop (but still above the threshold for a flattire), the wheel's rolling radius will be learned and the wheel speed ofthat wheel will be compensated for by the learned rolling radius. Thesame is true for large size tires, spare tire, roof loading and trunkloading. If the abnormal states are critical such as in a flat tirecase, the normal vehicle function like ISCS will be partially orcompletely shut off.

If there are no abnormal states detected in step 313, the systemproceeds to step 316 to compute the reference signals which will be usedin reference signal generator RSG (see U.S. Pat. No. 7,010,409). Noticethat the variables calculated in RSG may be used by various functionalunits such as SPC, GAD, DVD, etc.

In step 318, the vehicle body's roll and pitch attitudes with respect tothe sea level are calculated in GAD module. Although the engineeringdefinition of the vehicle body's roll and pitch attitudes are prettyobvious (which are simultaneously measured just like in the previousdefinitions of the road bank and slope), there are no mathematicalcharacterizations existed. Mathematically, Euler used sequentialrotation to define the angular distance between different frame systems.If the longitudinal axis is used for the roll axis, and lateral axis forthe pitch axis, then the Euler angles along those two axes are calledthe roll and pitch Euler angles respectively. Experimentally, theengineering definition (simultaneous measurement) of the vehicle body'sglobal roll and pitch angles are very close to the Euler attitudes(sequential rotational measurement) and the differences are negligible.For this reason, the roll and pitch angles defined here areinterchangeable with the Euler angles.

The Euler angles of the sensor cluster with respect to the sea level canbe related to the roll, pitch and yaw angular rate sensor signalsthrough the following coupled kinematics{dot over (θ)}_(sx)=θ_(sx)+[ω_(sy) sin(θ_(sx))+ω_(sz)cos(θ_(sx))]tan(θ_(sy)){dot over (θ)}_(sy)=ω_(sy) cos(θ_(sx))−ω_(sz) sin(θ_(sx))  (3)

The relationship depicted above reveals complicated nonlinear functionsand it indicates that a simple integration of the roll rate couldprovide accurate information about the roll attitude only if both thepitch and yaw rate are negligible, which means the vehicle is dominatedby roll motion; the roll attitude angle and yaw rate are negligible, thepitch attitude is limited; and, the pitch attitude angle is negligiblewith non-extreme pitch and yaw rates.

Similarly, the simple integration of the pitch rate could lead toaccurate prediction of the pitch attitude angle if the roll attitudeangle is negligible and the yaw rate is not extremely large. If theacceleration projected from the sensor frame to the vehicle body frameis defined as a_(bx), a_(by), the vehicle directional velocitiesmeasured on the vehicle body frame as ν_(bx), ν_(by), and the attitudesof the vehicle body with respect to the sea level as θ_(bx), θ_(by),then the following equations 4 hold.{dot over (ν)}=a_(bx)+ω_(bz)ν_(by) +g sin θ_(by){dot over (ν)}=a_(by)−ω_(bz)ν_(bx) +g sin θ_(bx) cos θ_(by)  (4)

In step 320, the vehicle body's relative attitudes with respect to itsaxles or the moving road frame are calculated. Those attitudes might becomputed as in U.S. Pat. Nos. 6,556,908, 6,684,140, and 6,631,317.

In step 322, the signals measured along the sensor frames aretransformed to signals along the moving road frames in the B2R module.If an IMU sensor cluster is used, the sensor signals might need to becompensated for frame different. For example, the sensor signals aremeant to be along the sensor frame directions are not necessary alongthe vehicle body frame directions or the directions of control interestssuch as the moving road frames. The angular differences betweendifferent frames can be mathematically characterized using Eulertransformations and using Euler angles. The Euler angles are defined asthe sequential rotation along an axis to move one frame system toanother frame system. When the Euler angle between the sensor frames₁s₂s₃ and the body frame b₁b₂b₃ is Δθ_(x), Δθ_(y), Δθ_(z), then theangular rates and accelerations of the vehicle body defined along thebody-fixed frame b₁b₂b₃ but at the sensor location may be calculatedusing the following matrix computation

$\begin{matrix}{\begin{bmatrix}\omega_{bx} \\\omega_{by} \\\omega_{bz}\end{bmatrix} = {{{{E\left( {{\Delta\theta}_{z},{\Delta\theta}_{y},{\Delta\theta}_{x}} \right)}\begin{bmatrix}\omega_{sx} \\\omega_{sy} \\\omega_{sz}\end{bmatrix}}\begin{bmatrix}a_{bx} \\a_{by} \\a_{bz}\end{bmatrix}} = {{E\left( {{\Delta\theta}_{z},{\Delta\theta}_{y},{\Delta\theta}_{x}} \right)}\begin{bmatrix}a_{sx} \\a_{sy} \\a_{sz}\end{bmatrix}}}} & (5)\end{matrix}$where the matrix E(•,•,•) is defined as the following for three Eulerangles θ₃, θ₂, θ₁

$\begin{matrix}{{E\left( {\theta_{3},\theta_{2},\theta_{1}} \right)} = \left\lbrack \begin{matrix}{\cos\;\theta_{3}\cos\;\theta_{2}} & {{\cos\;\theta_{3}\sin\;\theta_{2}\sin\;\theta_{1}} - {\sin\;\theta_{3}\cos\;\theta_{1}}} \\{\sin\;\theta_{3}\cos\;\theta_{2}} & {{\cos\;\theta_{3}\cos\;\theta_{1}} + {\sin\;\theta_{3}\sin\;\theta_{2}\sin\;\theta_{1}}} \\{{- \sin}\;\theta_{2}} & {\cos\;\theta_{2}\sin\;\theta_{1}}\end{matrix} \right.} \\\left. \begin{matrix}{{\cos\;\theta_{3}\sin\;\theta_{2}\cos\;\theta_{1}} + {\sin\;\theta_{3}\sin\;\theta_{1}}} \\{{\sin\;\theta_{3}\sin\;\theta_{2}\cos\;\theta_{1}} - {\cos\;\theta_{3}\sin\;\theta_{1}}} \\{\cos\;\theta_{2}\cos\;\theta_{1}}\end{matrix} \right\rbrack\end{matrix}$

Notice that the difference between the sensor frame and the body frameis mainly due to the sensor mounting errors. The sensor cluster mountingdirection errors may be obtained by converting the simultaneouslymeasured distances at the fixed points among the two frame systems toangular distance as in the definition of the moving road surface before.Mathematically, such a simultaneous measurement is different from thesequential definition of the Euler angles. However the differencesbetween those two measurements are not significant. For this reason, theΔθ_(x), Δθ_(y), Δθ_(z) used in this invention is interchangeable withthe engineering terminology such as the roll misalignment, pitchmisalignment and yaw misalignment. U.S. Pat. No. 6,782,315 provides amethod for determining Δθ_(x), Δθ_(y), Δθ_(z). If the vehicle bodymotion signals projected along the moving road frame is of interest, afurther Euler transformation can be conducted. When the engineering rollangle between the vehicle body and the axle is θ_(xr) (which can bedefined by using the suspension height differences between the left andright sides of the wheels and which is the same as the aforementionedrelative or chassis roll angle, see U.S. Pat. Nos. 6,556,908 and6,684,140), the engineering pitch angle between the vehicle body and theaxle is θ_(yr) (which can be defined by using the suspension heightdifferences between the front and rear axles and which is the same asthe aforementioned relative or chassis pitch angle, see U.S. Pat. Nos.6,556,908 and 6,684,140), the engineering roll angle between the axleand the moving road frame is θ_(wda) (which is non-zero only if thevehicle is experiencing an imminent rollover, see US patent publications2004/0064236 and 2004/0162654), then the vehicle body's motion variablesω_(mrfx), ω_(mrfy), ω_(mrfz), a_(mrfx), a_(mrfy), a_(mrfz) along themoving road frames may be computed as in the following

$\begin{matrix}{\begin{bmatrix}\omega_{mrfx} \\\omega_{mrfy} \\\omega_{mrfz}\end{bmatrix} = {{{{E\left( {0,\theta_{yr},{\theta_{xr} + \theta_{wda}}} \right)}\begin{bmatrix}\omega_{bx} \\\omega_{by} \\\omega_{bz}\end{bmatrix}}\begin{bmatrix}a_{mrfx} \\a_{mrfy} \\a_{mrfz}\end{bmatrix}} = {{E\left( {0,\theta_{yr},{\theta_{xr} + \theta_{wda}}} \right)}\begin{bmatrix}a_{bx} \\a_{by} \\a_{bz}\end{bmatrix}}}} & (6)\end{matrix}$

By using the features of the Euler transformation, ω_(mrfx), ω_(mrfy),ω_(mrfz), a_(mrfx), a_(mrfy), a_(mrfz) can be directly related to thesensor signals as in the following

$\begin{matrix}{\begin{bmatrix}\omega_{mrfx} \\\omega_{mrfy} \\\omega_{mrfz}\end{bmatrix} = {{{{E\left( {{\Delta\theta}_{z},{{\Delta\theta}_{y} + \theta_{yr}},{{\Delta\theta}_{x} + \theta_{xr} + \theta_{wda}}} \right)}\begin{bmatrix}\omega_{bx} \\\omega_{by} \\\omega_{bz}\end{bmatrix}}\begin{bmatrix}a_{mrfx} \\a_{mrfy} \\a_{mrfz}\end{bmatrix}} = {{E\left( {{\Delta\theta}_{z},{{\Delta\theta}_{y} + \theta_{yr}},{{\Delta\theta}_{x} + \theta_{xr} + \theta_{wda}}} \right)}\begin{bmatrix}a_{bx} \\a_{by} \\a_{bz}\end{bmatrix}}}} & (7)\end{matrix}$

Notice that in many cases, the motion variables such as accelerations atlocations other than the sensor location are of interests. For example,in this invention disclosure, the vehicle body accelerations a_(mrfrax),a_(mrfray), a_(mrfraz) at the vehicle rear axle location are ofinterests for lateral stability control and they can be furthertransformed according to the following computations:a_(mrfrax)=a_(mrfx) +p _(xsl2ra)(ω_(mrfy) ²+ω_(mrfz) ²)a_(mrfray)=a_(mrfy) −p _(xsl2ra)({dot over (ω)}_(mrfz)+ω_(mrfx)ω_(mrfy))a_(mrfraz)=a_(mrfz) +p _(xsl2ra)({dot over(ω)}_(mrfy)−ω_(mrfx)ω_(mrfz))  (8)where p_(sxl2ra) is the distance between the IMU sensor location and therear axle in the longitudinal direction. The sensor is assumed to belocated on the center line of the vehicle body. If such an assumption isnot true, extra terms will need to be added to the above computation.

In 324, the vehicle's directional velocities such as the vehiclelongitudinal velocity, lateral velocity, are calculated. The detaileddescription about such computations will be provided below.

In step 326, the vehicle's sideslip angle is computed. The detaileddescription about such a computation will be provided below.

In 328, the lateral and longitudinal tire forces, braking torques anddriving torques applied to the wheels are computed in the FATE unit byusing the available motion sensor information such as body motionvariables from IMU sensors, wheel speed sensors and actuator specificinformation such as the caliper brake pressure and the engine axletorque.

In 330, the normal loading from the road applied to the wheels at thewheel contact patches are computed in the NLD unit.

In 332, the vehicle's operational parameters such as the vehicle rollgradient, the vehicle loading and mass, the vehicle's c.g. height, etc.,are determined in the VPD unit.

In 334, the driving road parameters such as the road bank, slope,friction level, etc., are determined in the RPD unit. Some of thosecomputations might be found in U.S. Pat. No. 6,718,248 and US patentpublication 2004/0030475.

In 336, the driver's driving references are determined based on thedriver reference model DRM. One of the DRMs might be a bicycle modelused in finding the vehicle yaw reference, which is used to determinethe driver's intension. Notice that the tire forces reside on the movingroad plane, hence a driving reference model using tire force balancingmust work everything in the moving road frame. Let the desired motionvariables of the vehicle body at the vehicle body center of gravitylocation but projected to the moving road frame as a_(mrfcgxd),a_(mrfcgyd), ν_(mrfcgyd), ω_(mrfcgzd) for longitudinal acceleration,lateral acceleration, lateral velocity and yaw rate, satisfy thefollowing relationship based on a four-wheel vehicle model (here onlythe front wheel steering case is presented, for rear wheel steering andfour wheel steering case, similar equations may be obtained)I _(z){dot over (ω)}_(mrfcgzd) =F _(x1) l cos(γ+δ_(s))−F _(x2) lcos(γ−δ_(s))+(F _(x3) −F _(x4))t _(r) +F _(y1) l sin(γ+δ_(s))+F _(y2) lsin(γ−δ_(s))−F _(yr) l _(r)M _(t)a_(mrfcgxd)=(F _(x1) +F _(x2))cos(δ_(s))+F _(x3) +F _(x4)−(F _(y1)+F _(y2))sin(δ_(s))M _(t)a_(mrfcgyd)=(F _(xi) +F _(x2))sin(δ_(s))+(F _(y1) +F_(y2))cos(δ_(s))+F _(yr)  (9)where l=√{square root over (t_(f) ²+l_(f) ²)}, γ=a tan(t_(f)/l_(f)).M_(t) is the total vehicle mass; a_(mrfcgxd) and a_(mrfcgyd) are thedesired vehicle c.g. longitudinal and lateral acceleration projected onthe moving road frame; δ_(s) is the wheel steering angle, which may becalculated through the driver's steering wheel angle and the knownsteering gear ratio; F_(y1), F_(y2) and F_(yr) are the lateral forcesapplied to the front-left, front-right, rear axle (sum of the lateralforces of the rear-left and the rear right wheels) from the road.F_(x1), F_(x2), F_(x3), F_(x4) are the four longitudinal tire forces atthe front-left, the front-right, the rear-left and the rear-rightwheels. If the desired front wheels' sideslip angle is α_(mrffd) and therear wheels' sideslip angle is α_(mrfrd) (both of them are defined onthe moving road plane) then the desired vehicle sideslip angle, thesteering inputs and the desired yaw rate are related with each other asin the following:

$\begin{matrix}{{\alpha_{mrffd} = {\frac{v_{mrfcgyd}}{v_{mrfcgx}} + \frac{l_{f}\omega_{mrfcgzd}}{v_{mrfcgx}} - \delta_{s}}}{\alpha_{mrfrd} = {\frac{v_{mrfcgyd}}{v_{mrfcgx}} - \frac{l_{r}\omega_{mrfcgzd}}{v_{mrfcgx}}}}} & (10)\end{matrix}$

Using those wheel sideslip angles, the lateral tire forces may beexpressed asF _(y1) =c ₁α_(mrffd)F _(y2) =c ₂α_(mrffd)F _(yr) =c _(r)α_(mrfrd)  (11)where c_(i) is the cornering stiffness of the vehicle and by using thoseforces, thenI _(z){dot over (ω)}_(mrfcgzd)=a(δ_(s),ν_(mrfcgx))ω_(mrfcgzd)+b(δ_(s),ν_(mrfcgx))ν_(mrfcgyd) +c(δ_(s))F _(x)M _(t){dot over (ν)}_(mrfcgyd) =e(δ_(s),ν_(mrfcgx))ω_(mrfcgzd)+f(δ_(s),ν_(mrfcgx))ν_(mrfcgyd) +g(δ_(s))F _(x) +h(θ_(mrfx))  (12)

The above defined desired yaw rate and the desired lateral velocityneeds to satisfy the following equation for longitudinal direction forcebalancingy(F _(x),δ_(s),a_(mrfcgx))=c _(f)x(ν_(mrfcgyd),ω_(mrfcgzd),ν_(mrfcgs),δ_(s))  (13)where c_(f)=c₁+c₂, and functions y(•) and x(•) may be expressed as thefollowing

$\begin{matrix}{{x = {\left( {\frac{v_{mrfcgyd}}{v_{mrfcgx}} + \frac{l_{f}\omega_{mrfcgzd}}{v_{mrfcgx}} - \delta_{s}} \right){\sin\left( \delta_{s} \right)}}}{y = {{\left( {F_{x\; 1} + F_{x\; 2}} \right){\cos\left( \delta_{s} \right)}} + F_{x\; 3} + F_{x\; 4} - {M_{t}a_{mrfcgx}}}}} & (14)\end{matrix}$and this equation may be used to adaptively estimate the averagecornering stiffness experienced by the vehicle under the desired motionas in the following iterative schemec _(f)(k+1)=c _(f)(k)−ρω(k+1)[y(k)−c _(f)(k)x(k)]ΔT  (15)where ρ is the adaptive gain and ΔT is the sampling time of thecomputation. Notice that in the above DRM computation, the inputs arethe vehicle's longitudinal velocity projected on the moving road framebut computed at the c.g. of the vehicle, the measured longitudinalacceleration of the vehicle body projected on the moving road frame atc.g. of the vehicle body, the driver's steering wheel inputs. Thosevariables are directly related to the sensor measurements. The outputsare the desired yaw rate ω_(mrfcgzd), the desired lateral velocityν_(mrfcgyd), the updated tire cornering stiffness c_(f).

All the above calculated signals are fed into the ICSC module 44 and thearbitrated or prioritized or overridden control commands are then sentto the ECU or hardware electronics of the available actuators throughthe control signal represented by 342. The specific applications usingthose signals will be discussed in the following. The ISCS according toa first embodiment of the present invention intends to use differentialbraking to keep the vehicle moving in stable conditions regardless thedriver's inputs or the road surface conditions. The instability of thevehicle during a driver-initiated maneuver could be in roll direction(such as a RSC event), yaw direction (such as a YSC event), lateraldirection (such as a LSC event), or any combination of RSC, YSC and LSCevents.

For the LSC events case, the lateral instability of the vehicle happenswhen its lateral excursion relative to the driver's desired path isdivergent. For turning purpose, the vehicle has to have certain(absolute) lateral excursion (especially in the front axle), which isdefined through the driver's steering input. Even if the driver isrequesting a large steering input (which means a large absolute lateralexcursion), the vehicle could still be laterally stable (since thevehicle's relative lateral excursion could be small). During lateralinstability, the velocity of this relative lateral excursion is non-zeroand without crossing zero for a significant amount of time (for example,for more than 1 or 2 seconds). Mathematically, when a vehicle isnegotiating a path, the total vehicle's velocity coincides with thetangent direction of the path and the vehicle is laterally stable. Onthe other hand, if the vehicle's total velocity largely deviates fromthe tangent direction of the path defined by the driver's steeringinput, the vehicle is likely in the laterally instable mode. Consideringthe rear wheel does not have any steering angle (for a front wheelsteering vehicle), when the center of the rear axle negotiates the path,its total velocity must be along the longitudinal direction of themoving road frame. For this reason, the angle between the total velocityof the center of the rear axle and the vehicle's longitudinal directionare used as the measurements for the vehicle's lateral instability. Therear location is used in this invention as the location to define thevehicle's lateral instability. Since the vehicle's path always resideson the road surface or the moving road frame, the lateral instabilityalso needs to use the angle between the total velocity of the rear axleprojected on the moving road frame and the longitudinal direction of themoving road frame. Such an angle is a variation of the normally usedsideslip angle at the rear and is set forth as the variable β_(LSC).β_(LSC) is defined as in the following:

$\begin{matrix}{\beta_{LSC} = {\beta_{mrfra} = {\tan^{- 1}\left( \frac{v_{mrfray}}{v_{mrfrax}} \right)}}} & (16)\end{matrix}$

Ideally, the desired value for β_(LSC) is zero. For practicalimplementation purpose, a non-zero desired value β_(LSCd) is used. Theerror signalβ_(LSCe)=β_(LSC)−β_(LSCd)  (17)is used as a feedback signal to compute the control command forconducting LSC control. Let β_(db1) and β_(db2) be the two dead-bandsfor compute the torques necessary for counteracting the vehicle'slateral instability. The proportional portion of the feedback torqueM_(LSCP) can be computed as in the following

if during oversteer condition  if β_(LSCe) ≧ β_(db1) and β_(LSCe) ≦β_(db2)   M_(LSCP) = 0  else if β_(LSCe) < β_(db1) (18)   M_(LSCP) =G_(SP) ( β_(db1) − β_(LSCe) )  else   M_(LSCP) = G_(SP) ( β_(db2) −β_(LSCe) ) end

where G_(SP) is a control gain which could be an adaptive gain based onthe vehicle's dynamics. The over-steer condition of the vehicle can bedetermined based on the steering wheel information, the lateralacceleration information, the yaw rate information, the yaw errorinformation, the sideslip angle information, etc. One example of such anover-steer condition can be determined from the YSC yaw rate error. Thevariable dβ_(LSCe) is the derivative of β_(LSCe), which can be directlycomputed from β_(LSCe) or from the other signals. The variables dβ_(db1)and dβ_(db2) are the two dead-bands. The derivative portion of thefeedback torque M_(LSCD) can be computed as in the following:

if during oversteer condition  if d β_(LSCe) ≧ d β_(db1) and d β_(LSCe)≦ d β_(db2)   M_(LSCD) = 0  else if d β_(LSCe) < d β_(db1) (19)  M_(LSCD) = G_(SD) (d β_(db1) − d β_(LSCe))  else   M_(LSCD) = G_(SD)(d β_(LSCe) − d β_(LSCe)) endwhere G_(SD) is a control gain which could be an adaptive gain based onthe vehicle's dynamics. The under-steer condition of the vehicle can bedetermined based on the steering wheel information, the lateralacceleration information, the yaw rate information, the yaw errorinformation, the sideslip angle information and the like. One example ofan under-steer condition may be determined from the YSC yaw rate error.The final feedback torque M_(LSC) for LSC control can be obtainedthrough the following blendingM _(LSC)=λ₁ M _(LSCP)+λ₂ M _(LSCD)  (20)where the weights λ₁, λ₂ are two positive numbers less than 1 whichweight the relative importance of the proportional term and thederivative term in the final feedback torque. In certain drivingconditions, a constraint may be set forth as λ₁+λ₂=1.

The YSC yaw moment demand M_(YSC) may be generated through yaw rateerror feedback control. When ω_(mrfcgzd) is the desired or target yawrate which is determined in DRM module, ω_(mrfz) is the vehicle body'syaw rate but projected on the moving road frame. Then the vehicle yawrate error can be calculated asω_(mrfze)=ω_(mrfz)−ω_(mrfcgzd)  (21)

If ω_(mrfze)>ω_(zosthreshold)>0 together with the sign of the vehicle'ssideslip angle matching the turning direction of the vehicle, whereω_(zosthreshold) is a variable that reflects the threshold of thevehicle's over-steer characteristics, the vehicle is likely to be in anover-steer condition, i.e., the vehicle's yaw response exceeds thedriver's intention determined from the driver's steering wheel angle.Based on this, the following counteracting torque applied to the yawdirection of the vehicle may be computed so as to reduce the discrepancybetween the actual yaw rate and the desired yaw rate

if (ω_(mrfe) − ω_(zosthreshold) ≧ ω_(os) & &a_(mrfray) ≧ a_(yos) & &β_(mrfra) ≦ − β_(os)  || ω_(zosthreshold) − ω_(mrfe) ≧ ω_(os) &&a_(mrfray) ≦  −a_(yos) 0 & & β_(mrfra) ≧ β_(os) )   M_(YSC) = G_(OSYP)( ω_(zosthreshold) − ω_(mrfe) ) + (22)   G_(OSYD) ( d ω_(zosthreshold) −ω_(mrfe) ); else   M_(YSC) = 0where ω_(os), a_(yos), β_(os) are the dead-bands for the yaw rate errorbeyond threshold ω_(zosthreshold), the dead-band for the lateralacceleration, the dead-band for the sideslip angle at the rear axle;dω_(zosthreshold), {dot over (ω)}_(mrfe) are the derivatives of thethreshold ω_(zosthreshold) and the yaw rate error; G_(YPOS), G_(YDOS)are feedback control gains which are functions of the drivingconditions. M_(OS) is the control torque along the yaw direction thattries to regulate the yaw error during over-steer condition.

If ω_(mrfze)<ω_(zosthreshold)<0 with ω_(zosthreshold) together with thesign of the vehicle's sideslip angle matching the turning direction ofthe vehicle, where ω_(zosthreshold) is a variable that reflects thethreshold of the vehicle's under-steer characteristics, the vehicle islikely to be in a under-steer characteristics, i.e., the vehicle's yawresponse is below the driver's intension determined from the driver'ssteering wheel angle

f (ω_(mrfe) − ω_(zosthreshold) ≦ −ω_(us) & &a_(mrfray) ≧ a_(yus)  ||ω_(zosthreshold) − ω_(mrfe) ≦ ω_(us) & &a_(mrfray) ≦ −a_(yus) )   M_(US)= G_(YPUS) (ω_(zosthreshold) − ω_(mrfe) ) + (23)   G_(YDUS) ( dω_(zosthreshold) − ω_(mrfe) ); else   M_(US) = 0where ω_(us), a_(yus), β_(us) are the dead-bands for the yaw rate errorbeyond threshold ω_(zosthreshold), the dead-band for the lateralacceleration, the dead-band for the sideslip angle at the rear axle;dω_(zosthreshold) is the derivative of the threshold ω_(zosthreshold);G_(YPUS), G_(YDUS) are feedback control gains which are functions of thedriving conditions. M_(US) is the control torque along the yaw directionthat tries to regulate the yaw error during under-steer condition.

The RSC control is an over-steer type of control. The RSC controlcommand can be computed from the yaw torque based on the feedback signalof vehicle body-to-road roll angle. This torque may be set forth asM_(RSC).

Since for the different functions, there are different computations forcommanding the control torques applied to the vehicle's yaw directionthrough differential braking. Those control torques regulate differenterror signals such as the sideslip angle at the rear axle of the vehiclebut projected on the moving road plane (for LSC), the yaw error of thevehicle along the normal direction of the moving road plane (for YSC)and the relative roll angle between the vehicle body and the movingplane (for RSC). There is a need to arbitrate or prioritize or integratethose different computations to achieve the optimized integratedstability control performance. For under-steer control, since there isonly one control function (in YSC under-steer control), such anintegration is not necessary. However, for over-steer control, such anintegration is required. If M_(OS) and M_(US) are defined as the finallyarbitrated over-steer control torque and the under-steer control torque,then one of such integration scheme can be summarized as in thefollowing, where the weights γ₁, γ₂ and γ₃ are three positive numbersless than 1 that weight the relative importance among the three feedbacktorques:

if (M_(RSC) > 0 & &M_(LSC) > 0 & &M_(YSC) > 0 || M_(RSC) < 0 & &M_(LSC)< 0 & &M_(YSC) < 0 ) {  M_(OS) = γ₁M_(RSC) + γ₂M_(LSC) + γ₃M_(YSC) ;M_(US) = 0; } elseif (| M_(RSC) |> p_(rscth) & & | M _(LSC) |< p_(lscth)& & | M _(YSC) |< p_(yscth) ) {  M_(OS) = M_(RSC) ; M_(US) = 0; } elseif(| M_(RSC) |< p_(rscth) & & | M_(LSC) |> p_(lscth) & & | M_(YSC) |<p_(yscth) ) {  M_(OS) = M_(LSC) ; M_(US) = 0; } elseif (| M_(RSC) |<p_(rscth) & & | M_(LSC) |< p_(lscth) & & | M_(YSC) |> p_(yscth) ) { M_(OS) = M_(YSC) ; M_(US) = 0; } elseif (| M_(RSC) |> p_(rscth) & & |M_(LSC) |> p_(lscth) & & | M_(YSC) |< p_(yscth) ) {  [M_(OS) , i] =max(| M_(YSC) |,| M_(LSC) |); M_(OS) = M_(OS) sign(M_(i) ); M_(US) = 0;} elseif (| M_(RSC) |> p_(rscth) & & | M_(LSC) |< p_(lscth) & & |M_(YSC) |> p_(yscth) ) {  [M_(OS) , i] = max(| M_(RSC) |,| M_(YSC) |);M_(OS) = M_(OS) sign(M_(i) ); M_(US) = 0; } elseif (| M_(RSC) |<p_(rscth) & & | M_(LSC) |> p_(lscth) & & | M_(YSC) |> p_(yscth) ) { [M_(OS) , i] = max(| M_(LSC) |,| M_(YSC) |); M_(OS) = M_(OS) sign(M_(i)); M_(US) = 0; } else { (24)  [M_(OS) , i] = max(| M_(RSC) |,| M_(LSC)|,| M_(YSC) |); M_(OS) = M_(OS) sign(M_(i) ); M_(US) = 0; }

After the afore-mentioned torque M_(OS) or M_(US) has been computed, itmay be realized by building or releasing braking pressure on selectivewheels or wheel. Generally speaking, in over-steer case, the controlledwheel is the front outside wheel or both the front outside wheel and therear outside wheel, i.e., the brake pressure modification is requestedfor the front outside wheel or for the outside wheels; in under-steercontrol, the controlled wheel is the rear inside wheel or both theinside wheels, i.e., brake pressure modification is requested for therear inside wheel or for the inside wheels. Based on the aforementionedrule of thumb, various types of controls can be performed based on thevarious driving conditions. In the following discussion, a rear wheeldriving vehicle is assumed and the similar consideration holds for frontwheel driving or four wheel driving vehicles.

In the case of under-steering with throttle open, the engine torque isfirst reduced so as to regulate the under-steer yaw error. If the enginetorque reduction is not enough to bring the vehicle's yaw error belowcertain threshold, the rear inside wheel is braked and the brakepressure amount is computed based on the yaw error feedback torqueM_(US). For example, the brake pressure for the inside rear wheel needsto generate the following longitudinal slip ratio

$\begin{matrix}{\rho_{ir} = \frac{M_{US}}{t_{r}\kappa_{ir}N_{ir}}} & (25)\end{matrix}$where ρ_(ir) is the longitudinal slip-ratio of the inside rear wheel,t_(r) is the half track of the rear axle, κ_(ir), N_(ir) are the gainand the normal loading for the wheel at the inside rear location. If therequested insider rear wheel slip ratio |ρ_(ir)≧ ρ with ρ being theallowed minimum slip ratio at the rear wheels to prevent the rear end toloose. In some cases, when the vehicle's sideslip angle β_(LSC) is keptbelow certain threshold, both front inside and rear inside wheels mightbe applied brake pressure based on the following requested slip ratios

$\begin{matrix}{{{\rho_{ir} = \overset{\_}{\rho}};}{\rho_{if} = \frac{M_{US} - {\overset{\_}{\rho}t_{r}\kappa_{if}N_{if}}}{t_{r}\kappa_{if}N_{if}}}} & (26)\end{matrix}$

If after the above brake based under-steer control, the vehicle'sunder-steer yaw error is still big and the driver's steering input isstill increasing, the vehicle might have significant tire lateral forcesaturation in the front wheels. In this case, the vehicle may be sloweddown through additional braking. Such additional braking could beapplied to all the four wheels. Since the vehicle's turning radius isproportional to the vehicle's speed, hence slowing down the vehicle isindirectly helping reduce the under-steer of the vehicle. Notice thatwhenever the vehicle sideslip angle is beyond certain threshold, theafore-mentioned under-steer control request will be zeroed out. If theturning-off is not quick enough to change the actual caliper pressure,both under-steer control and over-steer control might happen brieflytogether. If the brake pressure apply to two wheels at the same axle,M_(US) might be realized through longitudinal force differential as inthe following, the yaw moment demand is developed through theside-to-side deviation of the longitudinal slip ratio between the twowheels

$\begin{matrix}{{\Delta\;\rho} = \frac{M_{US} - {1_{f}\left( {{\kappa_{1}N_{1}\lambda_{{fl}\;}} - {\kappa_{2}N_{2}\lambda_{f\; t}}} \right)}}{t_{f}\kappa_{2}N_{2}}} & (27)\end{matrix}$

In the case of under-steering with vehicle coasting, then the brakepressure will be first applied to the rear inside wheel. If theunder-steer yaw rate error cannot be significantly reduced, then afurther increase of the brake pressure in the front inside wheel (as in26)) will be conducted. If after the above brake based under-steercontrol, the vehicle's under-steer yaw error is still big enough,further braking will be applied to the outside wheels so as to furtherslow down the vehicle. Notice that whenever the vehicle sideslip angleis beyond certain threshold, the afore-mentioned under-steer controlrequest will be zeroed out.

In the case of under-steering with driver braking, the braking pressureis sent to the front inside wheel and the rear inside wheel until ABS isactivated. If the rear inside wheel enters ABS and the vehicle is stilldemanding large yaw error correction command, then part of the pressurefor the rear inside wheel will be sent to the front inside wheel. If thefront inside wheel enters ABS and the rear inside wheel is not in ABSand the yaw command is still high, part of the front inside wheelpressure will be redirected to the rear inside wheel. Notice thatwhenever the vehicle sideslip angle is beyond certain threshold, theafore-mentioned under-steer control request will be zeroed out. If sucha turning-off is not quick enough to change the actual caliper pressure,both under-steer control and over-steer control might happen brieflytogether.

In the case of over-steering with throttle open, the engine torquereduction is also conducted and at the same time a brake pressure basedon M_(OS) is sent to the front outside wheel.

In the case of over-steering with vehicle coasting, a brake pressurebased on M_(OS) is sent to the front outside wheel.

In the case of over-steering with driver braking, the braking pressureis applied to the front outside wheel and the front outside wheel isallowed to lock so as to kill significant yaw error and sideslip angle.

In the case of over-steering with driver braking, applying pressure tothe front outside wheel. If the front outside wheel is locked but theyaw command is still large, the rear inside wheel slip control isactivated (reducing the rear inside wheel slip ratio so as to increasethe lateral force at rear axle).

More detailed control scheme to realized the calculated feedback torqueM_(OS) and M_(US) can also be similarly developed based on thedrivetrain configuration.

The further details of the computation used in ISS will be providedhere.

The kinematics used in the ISS unit can be described by the followingequations for the body framedθ _(bx)=ω_(bx)+[ω_(bx) sin θ_(bx)+ω_(bz) cos θ_(bx)]tan θ_(by)dθ _(by)=ω_(by) cos θ_(bx)−ω_(bz) sin θ_(bx)dν _(bx)=a_(bx)+ω_(bz)ν_(by) +g sin θ_(by)dν _(bray)=a_(bray)−ω_(bz)ν_(bx) −g sin θ_(bx) cos θ_(by)  (28)where ν_(bray), a_(bray) are the lateral velocity and acceleration atthe rear axle location but projected on vehicle body-fixed frames.dθ_(bx), dθ_(by), dν_(bx), dν_(bray) are the variables whose theoreticvalues are the time derivatives of θ_(bx), θ_(by), ν_(bx), ν_(bray), butin reality due to sensor error or sensor uncertainties, they are notnecessarily equal to {dot over (θ)}_(bx), {dot over (θ)}_(by), {dot over(ν)}_(bx), {dot over (ν)}_(bray). In the sensor frame, the aboveequations can be rewritten asdθ _(sx)=ω_(sx)+[ω_(sy) sin θ_(sx)+ω_(sz) cos θ_(sx)]tan θ_(xy)dθ _(sy)=ω_(sy) cos θ_(sx)−ω_(sz) sin θ_(sx)dν _(sx)=a_(sx)+ω_(sz)ν_(sy) +g sin θ_(sy)dν _(sray)=a_(sray)−ω_(sz)ν_(sx) −g sin θ_(sx) cos θ_(xy)  (29)In the moving road frame, the following equations are truedθ _(mrfx)=ω_(mrfx)+[ω_(mrfy) sin θ_(mrfz) cos θ_(mrfx)]tan θ_(mrfy)dθ _(mrfy)=ω_(mrfy) cos θ_(mrfx)−ω_(mrfz) sin θ_(mrfx)dνmrfx=a_(mrfx)+ω_(mrfz)ν_(mrfy) +g sin θ_(mrfy)dνmrfray=a_(mrfray)−ω_(mrfz)ν_(mrfx) −g sin θ_(mrfx) cos θ_(mrfy)  (30)

In the following discussion, the details of directional velocitydetermination in ISS will be provided. First, start from the computationof the linear lateral velocity based on the bicycle model is performed.

Linear Lateral Velocity

Referring now to FIG. 8, the traditional bicycle model may be used todetermine, the yaw and lateral dynamics of a vehicle. This may beperformed using the following differential equationsI _(z){dot over (ω)}_(mrfz) =b _(f) F _(mrff) cos δ31 b _(r) F_(mrfr)−(I _(y) −I _(x))ω_(mrfy)ω_(mrfx) +Y _(z)M _(t)a_(mrfcgy) =F _(mrff) cos δ+F _(mrfr)  (31)where F_(mrff) and F_(mrfr) are the lateral forces applied to the frontaxle and rear axle through tires respectively; Y_(z) is the yawingmoment due to yaw stability control, which may be estimated based on thedesired yaw stability command and the estimated road surface μ; I_(x),I_(y), I_(z) are the roll, pitch and yaw momentum of inertia of thevehicle along the axes of the moving road frame which may beapproximated by those in the vehicle body frame; M_(t) is the vehicletotal mass; b_(f) is the distance from the vehicle center of gravity tothe front axle; b_(r) is the distance from the vehicle center of gravityto the rear axle; δ is the steering angle at the front wheels.

Let β_(mrff) and β_(mrfr) be the front and rear wheel sideslip anglesrespectively, which may be expressed as

$\begin{matrix}{{\beta_{mrflinf} = {\beta_{mrflincg} + \frac{b_{f}\omega_{mrfz}}{v_{mrfx}} - \delta}}{\beta_{mrflinr} = {\beta_{mrflincg} + \frac{b_{r}\omega_{mrfz}}{v_{mrfx}}}}} & (32)\end{matrix}$

For small wheel sideslip angles, i.e.|β_(mrff)|≦ β _(f)|β_(mrfr)|≦ β _(r)  (33)the lateral forces applied to the front axle and the rear axle may beapproximated as the following linear relationshipF _(mrff) ≈−c _(f)β_(mrff)F _(mrfr) ≈−c _(r)β_(mrfr)  (34)where β _(f) and β _(r) are front and rear wheel slip angle upper boundsto guarantee the linear relationships in (34), and c_(f) and c_(r) arethe cornering stiffness of the front and rear tires respectively. c_(f)and c_(r) usually vary with the road condition and the vehicle operationcondition. Due to the steering angle and large loading towards the frontaxle, the front wheel sideslip angle β_(mrff) usually exceeds the linearrange of the tire force much earlier than the rear axle tires. Notice assoon as (33) is satisfied, (31)-(34) are true. If the vehicle isoperated in its nonlinear dynamics range, using (34) with fixed valuesfor c_(f) and c_(r) is no longer close to the true wheel sideslipangles. However the computation may still be used for other computationpurpose, for example, used in the switch logic for other computations.For this reason, the following linear sideslip angles may be definedregardless of whether the vehicle is operated in its linear dynamicsrange or its nonlinear dynamics range

$\begin{matrix}{{\beta_{mrflinf} = \frac{F_{mrff}}{c_{f}}}{\beta_{mrflinr} = \frac{F_{mrfr}}{c_{r}}}} & (35)\end{matrix}$where the lateral tire forces may be calculated as in the following,which are true for all the driving conditions (independent of roadsurface mu level, the aggressiveness of the driver's driving input, andif the tires entering their nonlinear ranges, etc.)

$\begin{matrix}{{\rho_{mrff} = \frac{{I_{z}{\overset{.}{\omega}}_{mrfz}} + {\left( {I_{y} - I_{x}} \right)\omega_{mrfy}\omega_{mrfx}} - Y_{z} + {b_{r}M_{t}a_{mrfv}}}{\left( {b_{f} + b_{r}} \right)\cos\;\delta}}{F_{mrjr} = \frac{{{- I_{z}}{\overset{.}{\omega}}_{mrfz}} + {\left( {I_{y} - I_{x}} \right)\omega_{mrfy}\omega_{mrfx}} - Y_{z} + {b_{f}M_{t}a_{mrfy}}}{\left( {b_{f} + b_{r}} \right)}}} & (36)\end{matrix}$

In step 700 the sensor information may be transformed into a body frameof reference. The raw rear wheel sideslip angle β_(mrflinrraw) isdetermined in step 702 and is used here as an estimation and controlreference. It may be further expressed as the following:β_(mrflinrraw) =p _(yawgrad)a_(mrfy) −p _(yawacccoef){dot over(ω)}_(mrfz) −p _(coupling)ω_(mrfy)ω_(mrfx) +p _(yawtorq) Y _(z)  (37)where the four composite parameters, called yaw gradient, yawacceleration coefficient, coupling coefficient and yaw torque gainrespectively, may be related to the vehicle parameters as in thefollowing:

$\begin{matrix}{{p_{yawgrad} = \frac{b_{f}M_{t}}{\left( {b_{f} + b_{r}} \right)c_{r}}}{p_{yawacccoef} = \frac{I_{z}}{\left( {b_{f} + b_{r}} \right)c_{r}}}{p_{coupling} = \frac{\left( {I_{y} - I_{x}} \right)}{\left( {b_{f} + b_{r}} \right)c_{r}}}{p_{yawtorq} = \frac{1}{\left( {b_{f} + b_{r}} \right)c_{r}}}} & (38)\end{matrix}$

The four composite parameters may also be estimated through the fittingof the empirical vehicle data to (37) during linear vehicle dynamics.This can also be done in real-time adaptively.

Those parameters may also be calculated based on vehicle testing data.For example, using a Least Square Parameter identification for themaneuvers within the linear tire force range, the calculatedβ_(mrflinrraw) may be used to fit the measured sideslip angle.

In order to take account of the effect lateral load transfer, a loadtransfer correction factor is delivered in step 704,

if (| θ_(xr) |≦0.75 p_(rollgrad)) {${\beta_{mrflinrraw} = \frac{\beta_{mrflinrraw}}{1 - {p_{csxmax}\left( {{\theta_{xr}}\text{/}p_{rollgrad}} \right)}^{2}}};$} (39) else {${\beta_{mrflinrraw} = \frac{\beta_{mrflinrraw}}{1 - {0.5625\mspace{11mu} p_{csxmax}}}};$}

The final linear sideslip angle may be calculated in step 706 in thefollowing:β_(mrflinr) =p _(yawmdl)β_(mrflinr)+(1−p _(yawmdl))β_(mrflinrraw)  (40)where θ_(xr) is the relative roll angle calculated in RSC, whichreflects the lateral load transfer, p_(rollgrad) is the roll gradientand p_(csxmax) is the maximum percentage change of the corneringstiffness reduction due to lateral load transfer. The linear lateralvelocity based on the linear sideslip angle in step 708 is defined asν_(mrflinray)=ν_(mrfx) tan(β_(mrflinr))  (41)

If an equivalent cornering stiffness is defined at the rear wheelc_(eqr) in the following

$\begin{matrix}{c_{eqr} = \frac{F_{mrfx}}{\beta_{mrfy}}} & (42)\end{matrix}$the equivalent cornering stiffness ratio in step 710 may be computed as

$\begin{matrix}{S = \frac{c_{r}}{c_{eqr}}} & (43)\end{matrix}$

Since c_(r) is proportional to the surface friction level μ (where μ=1)and c_(eqr) is proportional to the actual road surface μ level, theequivalent cornering stiffness ratio indirectly relates to the roadsurface μ, although the actual function would be rather complicated.

If the vehicle's true (nonlinear) sideslip angle β_(mrfr) is known, thenthe aforementioned equivalent cornering stiffness ratio may becalculated as in the following:

$\begin{matrix}{S = \frac{\beta_{mrfr}}{\beta_{mrtlinr}}} & (44)\end{matrix}$

However, β_(mrfr) is not known and needs to be calculated first, {dotover (β)}_(mrfr) is known.

A good computation strategy would be working on {dot over (β)}_(mrfr)and using washout filter to obtain some rough computation of S, andusing such a calculated S in some other conditions related to the roadsurface μ. The raw value S_(raw) of the equivalent cornering stiffnessratio S is computed through a washout filter and the computation may besummarized as in the following

if (|β_(mrflinr)|>p_(minlatvel)) v_(temp)= β_(mrflinr)v_(mrfx); else if (β_(mrflinr)>=0 && β_(mrflinr) ≦ p_(minlatvel)) v_(temp)=p_(minlatvel)v_(mrfx); (45) else v_(temp)=−p_(minlatvel)v_(mrfx);${S_{raw} = {{\left\lbrack {\gamma_{sintcoef} - \frac{\left( {{{\overset{.}{v}}_{mrfx}\beta_{mrflinr}} + {v_{mrfx}{\overset{.}{\beta}}_{mrflinr}}} \right)\Delta\; T}{v_{temp}}} \right\rbrack\mspace{11mu} S_{raw}} + \frac{{\overset{.}{v}}_{mrfy}\Delta\; T}{v_{temp}}}};$where γ_(sintcaef) is the washout filter coefficient, p_(minlatvel) isthe lower bound of the linear sideslip angle β_(mrflinr), ΔT is thesampling time, ν_(mrfx) is the longitudinal velocity of the vehicle.

Considering at low vehicle speeds, the above computation may becontaminated by the signal noises and the other errors, hence at lowvehicle speed, the equivalent cornering stiffness ratio is set to 1.Since S also reflects the road surface μ, thus during known road surfacecases, S needs to be limited by the known value. Therefore,

if (v_(mrfx < psmspd) ) S_(raw) = 1; else { if ( μ_(max) > p_(smmu))(46)${S_{raw} = {\min\mspace{11mu}\left( {\frac{1}{p_{smmu}},{\max\mspace{11mu}\left( {S_{raw},1} \right)}} \right)}};$else${S_{raw} = {\min\mspace{11mu}\left( {\frac{1}{p_{smmu}},{\max\mspace{11mu}\left( {S_{raw},1} \right)}} \right)}};$}

The final equivalent cornering stiffness ratio is obtained by feedingthe computed raw value through a low-pass filter in the following:S=d _(lpf1) S+n _(lpf1) S _(raw)  (47)where n_(lpf1), d_(lpf1) are coefficients for the low pass filter.

Lateral Velocity and Its Reference

DVD schemes are set forth below. The first, second, or combination ofboth, may be used. The first scheme is illustrated in step 711 a anduses a longitudinal kinematics constraint. If the longitudinal velocityis known, then the third equation in (29) or (30) becomes redundant.That is, the third equation in (29) or (30) may be eliminated. However,a total elimination of such an equation would not be desirable sincepotential useful information may be lost. A case where the vehicle isdriven steady state on a constant radius turn on a level ground isillustrated. In such a driving case, the acceleration balancing throughthe first velocity equation in (29) or (30) may actually be used toconstrain the lateral velocity (the so-called centrifugal acceleration)

$\begin{matrix}{{a_{mrfx} = {{- v_{mrfy}}\omega_{mrfz}}}{or}{v_{mrfy} = {- \frac{a_{mrfx}}{\omega_{mrfz}}}}} & (48)\end{matrix}$

Therefore, the first velocity equation may be used as a constraint forthe estimated lateral velocity. Such a constraint is called thelongitudinal kinematics constraint, which is expressed ask_(x)(ν_(mrfray),ν_(mrfraz))=ā_(mrfx)+ω_(mrfz)ν_(mrfay)−ω_(mrfy)ν_(mrfraz)−{dotover (ν)}_(mrfx)  (49)

Notice that the true lateral velocity and longitudinal velocity shouldsatisfyk _(x)(ν_(mrfray),ν_(mrfraz))=0  (50)and good estimations {circumflex over (ν)}_(mrfx) and {circumflex over(ν)}_(mrfray) of ν_(mrfx) and ν_(mrfray) should make |k_(x)(ν_(mrfray),ν_(mrfraz))| as small as possible. The estimation error is:e _(mrfy)=ν_(mrfray)−{circumflex over (ν)}_(mrfray)e _(mrfz)=ν_(mrfraz)−{circumflex over (ν)}_(mrfraz)  (51)

By using the kinematics constraint shown in (51), the followingestimation scheme may be formulated as:{circumflex over ({dot over(ν)}_(mrfray)=ā_(mrfray)−ω_(mrfz)ν_(mrfx)+ω_(mrfx){circumflex over(ν)}_(mrfraz) +G ₁ k _(x)({circumflex over (ν)}_(mrfray),{circumflexover (ν)}_(mrfraz)){circumflex over ({dot over(ν)}_(mrfraz)=ā_(mrfraz)−ω_(mrfy)ν_(mrfx)−ω_(mrfx){circumflex over(ν)}_(mrfray) +G ₂ {circumflex over (k)} _(x)({circumflex over(ν)}_(mrfray),{circumflex over (ν)}_(mrfraz))  (52)where G₁ and G₂ are gains needed to be properly chosen. The errordynamics for estimation scheme (52) satisfiesė _(mrfy)=ω_(mrfx) e _(mrfz) −G ₁(ω_(mrfy) e _(mrfz)−ω_(mrfz) e _(mrfy))ė _(mrfz)=−ω_(mrfx) e _(mrfy) −G ₂(ω_(mrfy) e _(mrfz)−ω_(mrfz) e_(mrfy))  (53)

The gains G₁ and G₂ may then be selected such that the errors in (59)approach zero. If the following function is chosen

$\begin{matrix}{V = {\frac{1}{2}\left( {e_{mrfy}^{2} + e_{mrfz}^{2}} \right)}} & (54)\end{matrix}$then its derivative along the error dynamics (53) may be calculated as{dot over (V)}=G ₁ω_(mrfz) e _(mrfy) ² −G ₂ω_(mrfy) e _(mrfz) ² −G₁ω_(mrfy) e _(mrfx) e _(mrfy) G ₂ω_(mrfz) e _(mrfy) e _(mrfz)  (55)

If a positive number ρ and the gains G₁ and G₂ are chosen in thefollowingG ₁=−ρω_(mrfz)G ₂=ρω_(mrfy)  (56)then (55) can be made negative{dot over (V)}=−ρ(ω_(mrfz) e _(mrfy)−ω_(mrfy) e _(mrfz))²≦0  (57)which implies the choice of gains in (56) will keep the rate change ofthe estimation error decreasing. Hence, (52) provides a usefulconstruction of the lateral velocity, which utilizes feedbackinformation.

If the lateral angle Θ_(Xσ) is defined as:

$\begin{matrix}{\Theta_{x\;\sigma} = {\int_{t_{1}}^{\sigma}{{\omega_{mrfx}(\tau)}\ {\mathbb{d}\tau}}}} & (58)\end{matrix}$and considering ν_(mrfraz) is close to zero and is negligible, equation(52) may be further simplified as:

$\begin{matrix}{{v_{mrfray}\left( t_{2} \right)} = {\sec\;\Theta_{{xt}_{2}}\left\{ {{v_{mrfray}\left( t_{1} \right)} + {\int_{t_{1}}^{\tau_{2}}{\left\lbrack {{\left( {{\overset{\_}{a}}_{mrfray} - {\omega_{mrfz}v_{mrfx}} - {\rho\;\omega_{sz}{k_{x}\left( {{\hat{v}}_{mrfray},{\hat{v}}_{mrfraz}} \right)}}} \right)\cos\;\Theta_{x\;\sigma}} - {\left( {{\overset{\_}{a}}_{mrfraz} + {\omega_{mrfy}v_{mrfx}} + {\rho\;\omega_{sy}{k_{x}\left( {{\hat{v}}_{mrfray},{\hat{v}}_{mrfraz}} \right)}}} \right)\sin\;\Theta_{x\;\sigma}}}\  \right\rbrack{\mathbb{d}\sigma}}}} \right\}}} & (59)\end{matrix}$

In the second scheme set forth, a road constraint alignment (RCA) instep 711 b is determined. An RCA presumes the vehicle cannot lift offfrom the ground for a long period of time. Hence, the vertical velocitymust be very small and its derivative must not have significant lowfrequency content. If the vertical velocity is neglected, then thevertical velocity equation becomes redundant. However, a totalelimination of such an equation would be bad since potential usefulinformation is lost. Considering a case where the vehicle is in adynamic turn on a smooth road surface and the vehicle has no-zero rollmotion, the vehicle lateral velocity may be constrained in the followingequation (the so-called centrifugal acceleration):

$\begin{matrix}{{{\omega_{mrfx}v_{mrfray}} = {a_{mrfraz} + {\omega_{mrfy}v_{mrfx}}}}{or}{v_{mrfy} = \frac{a_{mrfraz} + {\omega_{mrfy}v_{mrfx}}}{\omega_{mrfx}}}} & (60)\end{matrix}$

Generally speaking, RCA can be described as:k _(z)(ν_(mrfx),ν_(mrfray))=LPF[ā_(mrfraz)+ω_(mrfy)ν_(mrfx)−ω_(mrfx)ν_(mrfray)]=0  (61)where LPF stands for the low-pass filtering. This may be referred to asa vertical kinematics constraint. For estimated velocities, (61) may bethought of as an enforcement mechanism for compensating potential errorsources. Denote the estimated longitudinal and vertical velocities as{circumflex over (ν)}_(mrfx) and {circumflex over (ν)}_(mrfray), theestimation errors ase _(mrfx)=ν_(mrfx)−{circumflex over (ν)}_(mrfx)e _(mrfy)=ν_(mrfray)−{circumflex over (ν)}_(mrfray)  (62)

One of the estimation schemes may be described as in the following:{circumflex over ({dot over (ν)}_(mrfx)=ā_(mrfx)+ω_(mrfz){circumflexover (ν)}_(mrfray) +H ₁({circumflex over (ν)}_(mrfx)−ν_(mrfx))+H ₂ k_(z)({circumflex over (ν)}_(mrfx),{circumflex over (ν)}_(mrfray)){circumflex over ({dot over (ν)}_(mrfray)=ā_(mrfray)−ω_(mrfz){circumflexover (ν)}_(mrfx) +H ₃ k _(z)({circumflex over (ν)}_(mrfx),{circumflexover (ν)}_(mrfray))  (63)where H₁, H₂ and H₃ are gains needed to be properly chosen. Notice thatν_(sx) is calculated from wheel speed sensor signals together withcertain calculated signals, which means it is independent ofcomputations in (65). The error dynamics for the estimation scheme (63)satisfiesė _(mrfx)=ω_(mrfz) e _(mrfy) −H ₁ e _(mrfx) −H ₂ LPF[ω _(mrfx) e_(mrfy)−ω_(mrfy) e _(mrfx)]ė _(mrfy)=−ω_(mrfz) e _(mrfx) −H ₂ LPF[ω _(mrfx) e _(mrfy)−ω_(mrfy) e_(mrfx)]  (64)

For analysis simplicity, the LPF may be removed.

Let

$\begin{matrix}{V = {\frac{1}{2}\left( {e_{mrfx}^{2} + e_{mrfy}^{2}} \right)}} & (65)\end{matrix}$then the derivative of V along the error dynamics (65) may be calculatedas{dot over (V)}=−H ₁ e _(mrfx) ² −H ₂ω_(mrfx) e _(mrfy) e _(mrfx) +H₂ω_(mrfy) e _(mrfx) ² −H ₃ω_(mrfx) e _(mrfy) ² +H ₃ω_(mrfy) e _(mrfy) e_(mrfx)  (66)

IfH₁>0H ₂=−ρω_(mrfy)H ₃=ρω_(mrfx)  (67)then{dot over (V)}=−H ₁ e _(mrfx) ²−ρ(ω_(mrfz) e _(mrfy)−ω_(mrfy) e_(mrfz))²≦0  (68)which implies that the choice of gains in (67) will keep rate change ofthe estimation error decrease. By replacing the estimated longitudinalvelocity with the external longitudinal velocity (for example, fromwheel speed sensors), the following provides a construction of theintended estimation of the lateral velocity

$\begin{matrix}{{{v_{mrfray}\left( t_{2} \right)} = {{{- {v_{mrfx}\left( t_{2} \right)}}\tan\;\left( \Theta_{{zt}_{2}} \right)} + {{\sec\left( \;\Theta_{{zt}_{2}} \right)}\left\{ {{v_{mrfray}\left( t_{1} \right)} + {\int_{t_{1}}^{\tau_{2}}{\left\lbrack {{\left( {{\overset{\_}{a}}_{mrfx} - {\rho\;\omega_{mrfy}{k_{z}\left( {{\hat{v}}_{mrfx},{\hat{v}}_{mrfray}} \right)}}} \right)\sin\;\left( \Theta_{z\;\sigma} \right)} + {\left( {{\overset{\_}{a}}_{mrfray} + {\rho\;\omega_{mrfx}{k_{z}\left( {{\hat{v}}_{mrfx},{\hat{v}}_{mrfray}} \right)}}} \right){\cos\left( \;\Theta_{z\;\sigma} \right)}}} \right\rbrack\ {\mathbb{d}\sigma}}}} \right\}}}}{where}} & (69) \\{\Theta_{zt} = {\int_{t_{1}}^{t}{{\omega_{mrfz}(\tau)}\ {\mathbb{d}\tau}}}} & (70)\end{matrix}$

Notice that the above two schemes can be used only when the dynamicsmeasured by the IMU sensors experiences large angular rates. If theangular rates are small, the afore-mentioned constraints is no longeruseful. For this reason, the computation described before cannot bedirectly used to compute the lateral velocity of the vehicle body at therear axle but projected on the moving road frame. However, they couldserve as a reference lateral velocity.

In step 712, the reference lateral velocity is computed. Consideringvertical velocity is small, the vertical velocity equation in theprevious RCA can be dropped. Therefore,dν_(mrfray)=ā_(mrfray)−ω_(mrfz)ν_(mrfx)−ρω_(mrfz)(ā_(mrfx)+ω_(mrfz){circumflexover (ν)}_(mrfray)−{dot over (ν)}_(mrfx))  (71)

Equation (71) is accurate enough when the vehicle does not havesignificant heave and roll motion. If the vehicle is driven on a bumpyroad with significant roll motion, the cross product termω_(mrfx)ν_(mrfraz) needs to be estimated and add to (71) so as to removethe error.

Equation (71) may be integrated to obtain a signal which is a referencesignal for the lateral velocity at the rear axle and projected on themoving road frames Due to the computational errors in the attitudes andthe sensor errors, both the integration rate and the initial conditionwill be changed based on certain reliable computations.

One of such reliable signals is the linear sideslip angle of the vehicleat its rear axle, which is already calculated above. The magnitude ofsuch a variable may be calculated a in the followingβ_(mrflinrmag) =p _(dlpflbetam)β_(mrflinrmag)+(1−p_(dlpflbetam)|β_(mrflinr)|)  (72)

The roll attitude of the moving road frame θ_(mrfx) may havecomputational errors, the integration coefficient used will be adaptedbased on the magnitude of θ_(mrfx) as in the following

if (| θ_(mrfx) |≦ θ₁ )  γ_(intcoef) = p_(intcoef1); else if (θ₁ ≦|θ_(mrfx) |≦ θ₂ )  γ_(intcoef) = p_(intcoef2); else if (θ₂ ≦| θ_(mrfx) |≦θ₃ ) (73)  γ_(intcoef) = p_(intcoef3); else if (θ₂ ≦| θ_(mrfx) |≦ θ₃ ) γ_(intcoef) = p_(intcoef4); else  γ_(intcoef) = p_(intcoef5);

The further adaptation of the integration rate is conducted based on theindication of the road surface μ reflected by the maximum accelerationof the vehicle and the magnitude of the equivalent cornering stiffnessratio computed above

$\mu_{\max} = {{n_{{lpf}\mspace{11mu} 2}\mu_{\max}} + {\frac{d_{{lpf}\mspace{11mu} 2}}{g}\sqrt{a_{mrfrax}^{2} + a_{mrfray}^{2} + a_{mrfraz}^{2}}}}$if ( (μ_(max) > p_(muminhighmu) or S < p_(smaxhighmu) ) and |a_(mrfray)|≦ p_(minlata) ) (74) { γ_(intcoef) = min(γ_(intcoef),γ_(intcoeffast)); γ

The conditional integration of (71) may be conducted in the following

if ( ( ( β_(mrflinrmag) ≧ p_(smlinb) & & S ≦ p_(minslowmu) )  or ω_(mag)≧ p_(smrat) || | d_(swa) | > p_(smswa) ) & & v_(mrfx) ≧ p_(smspd) ) { k_(cgain) = k_(gain) ( v_(mrfx) ≧ p_(gainswitchspd) );  k_(cx) =a_(mrfrax) + w_(mrfz) v_(mrfrefy) − v_(mrfx) ;  if(k_(cx) ≧ k_(cxmax) )(75)   k_(cx) = k_(cxmax) ;  if(k_(cx) ≦ −k_(cxmax) )   k_(cx) =−k_(cxmax) ;  v_(mrfrefy) = v_(mrfrefy) γ_(intcoef) + (a_(mrfray) −w_(mrfz) v_(mrfx) − k_(cgain) w_(mrfz) k_(cx)); }

Let the final computation of the lateral velocity at the rear axle beν_(mrfray). The above calculated lateral velocity reference may bebounded by the final computation of ν_(mrfray). The followingconditioning will be conducted if the final computation of ν_(mrfray)exceeds the magnitude of the final computation ν_(mrfrefy), thereference value will be gradually adjusted to approach the finalcomputation ν_(mrfray)

if ( ( ν_(mrfrefy) ≧ ν_(mrfray) and ν_(mrfray) ≧ 0 )  or ( ν_(mrfrefy) ≧ν_(mrfray) and ν_(mrfray) ≦ 0 ) ) (76)  ν_(mrfrefy) = ν_(mrfray) +(ν_(mrfrefy) − ν_(mrfray))/ p_(rho);

A further conditioning will be conducted at linear sideslip range, whichassigns the computation to the linear velocity calculated from thelinear sideslip angle

if ( ( ν_(mrfrefy) ν_(mrflinray) < 0 or (ν_(mrflinr) ≧ 0 and ν_(mrfrefy)≦ ν_(mrflinray))  or (ν_(mrflinr) ≦ 0 and ν_(mrfrefy) ≧ ν_(mrflinray)))and (S ≦ p_(minslowmu))) (77) {    ν_(mrfrefy) = ν_(mrflinray); }

A further magnitude limitation is necessary

if (ν_(mrfrefy) > 0)  ν_(mrfrefy) = min(min(p_(betabound)|ν_(mrfx) |,p_(maxlatvel))), ν_(mrfrefy)); (78) else  ν_(mrfrefy) = max(max( −p_(betabound)|ν_(mrfx) |, − p_(maxlatvel))), ν_(mrfrefy));

If the conditions in (75) are not satisfied, the reference lateralvelocity will be switched to the linear lateral velocity

else  { (79)     ν_(mrfrefy) = ν_(mrflinray);  }

Now the low frequency portion ν_(mrfssy) of the lateral velocity at therear axle and on the moving road frame in step 714 may be determined.This may be done through a steady state recovery filter in the followingν_(mrfssy) =d _(ssc)ν_(mrfssy) +n _(ssc)ν_(mrfrefy)  (80)where d_(ssc), n_(ssc) are the filter coefficients.

Another method to obtain the low frequency portion ν_(mrfssy) is throughthe following initial condition resetting

 ν_(mrfssy) = d_(ssc)ν_(mrfssy) + n_(ssc)ν_(mrfrefy) if ((ν_(mrfray)ν_(mrflinry) < 0  or (ν_(mrflinry) ≧ 0 and ν_(mrfray) ≦ν_(mrflinry))  or (ν_(mrflinry) ≦ 0 and ν_(mrfray) ≧ ν_(mrflinry))  )and (S ≦ p_(minslownmu))) (81) {  ν_(mrfssy) = ν_(mrflinry) −ν_(mrfdyny); }

Now the computation of the dynamic portion of the lateral velocity atthe rear axle on the moving road frame in step 716 is considered. Thismay be referred to as the high frequency portion. The derivative of sucha velocity may be expressed as in the followingdν _(mrfy)=ā_(mrfy)−ω_(mrfz)ν_(mrfx)+ω_(mrfx)ν_(mrfz)  (82)

Considering the vertical velocity is small enough, the following is truedν _(mrfy)=ā_(mrfy)−ω_(mrfz)ν_(mrfz)  (83)

Using a anti-drift integration, the dynamic portion ν_(mrfdyny) of thelateral velocity ν_(mrfray) may be calculated as in the followingν_(mrfdyny) =d _(adi)ν_(mrdyny) +n _(adi) dν _(mrfy)  (84)

Since the potential errors in the computation in (83), a computationcombining (84) with initial condition enforcement is conducted as in thefollowing

ν_(mrfdyny) = d_(adi)ν_(mrfdyny) + n_(adi)dν_(mrfray) if ((ν_(mrf)ν_(mrflinry) < 0  or (ν_(mrflinry) ≧ 0 and ν_(mrfray) ≦ν_(mrflinry))  or (ν_(mrflinry) ≦ 0 and ν_(mrfray) ≧ ν_(mrflinry))  )and (S ≦ p_(minslowmu))) (85) {  ν_(mrfdyny) = ν_(mrflinry) −ν_(mrfssy); }

In step 718 the final lateral velocity may be determined by combiningthe steady state and dynamic lateral velocity. A variation of (85) maybe further conducted by using a smooth ramping to replace a suddenswitch

ν_(mrfdyny) = d_(adi)ν_(mrfdyny) + n_(adi)dν_(mrfray) if ((ν_(mrf)ν_(mrflinry) < 0  or (ν_(mrflinry) ≧ 0 and ν_(mrf) ≦ν_(mrflinry))  or (ν_(mrflinry) ≦ 0 and ν_(mrf) ≧ ν_(mrflinry))  ) and(S ≦ p_(minslowmu))) (86) {  ν_(mrfdyny) = ν_(mrflinry) − ν_(mrfssy) +(ν_(mrfdyny) − ν_(mrflinry) + ν_(mrfssy))/ p_(rho); }

A further variation is the following

if (( ν_(mrf)ν_(mrflinry) < 0  or (ν_(mrflinry) ≧ 0 and ν_(mrf) ≦ν_(mrflinry))  or (ν_(mrflinry) ≦ 0 and ν_(mrf) ≧ ν_(mrflinry))  ) and(S ≦ p_(minslowmu))) (87)  ν_(mrfdyny) = ν_(mrflinry) − ν_(mrfssy) +(ν_(mrfdyny) − ν_(mrflinry) + ν_(mrfssy))/ p_(rho); else  ν_(mrfdyny) =d_(adi)ν_(mrfdyny) + n_(adi)dν_(mrfray);

The final lateral velocity at the rear axle and on the moving road framemay be used to control various vehicle systems including but not limitedto a yaw control system and other dynamic control systems.

Longitudinal Velocity Determination

In this embodiment, the vehicle longitudinal velocity is determinedbased on the compensated wheel speed sensor signals, the IMU sensorcluster outputs and the computed signals from the other modules in ISSunit, the wheel control status (in ABS, TCS, RSC, AYSC, or driverbraking), engine torque and throttle information. The vehiclelongitudinal velocity considered here is defined along the longitudinaldirection of the moving road frame. The wheel speeds are the linearvelocities which are projected on the instantaneous plane defined by themoving road frame (the longitudinal and lateral axle of the moving roadframe). The algorithms and methods presented here reduce errors inexisting longitudinal velocity computations used in brake controlsystems (ABS and TCS) and the vehicle stability control systems (such asESC and RSC), which are based on the traditional ESC sensor set or theRSC sensor set.

The vehicle longitudinal velocity is an important variable used forvehicle dynamics controls. For example, the ABS and TSC brake controlsactivate the individual brake based on the longitudinal slip ratio ofthe corresponding wheel. The longitudinal slip ratio at a specificcorner measures the relative difference between the velocity of thevehicle body at the corresponding corner and the linear velocity of thecenter of the corresponding wheel. Slip ratios are also used in ISCSfunctions such as RSC, YSC and LSC.

Another usage of the longitudinal velocity is to calculate the vehiclesideslip angle which is obtained by dividing the calculated lateralvelocity at specific location of the vehicle body (for example at thevehicle center of gravity or at the middle of the rear axle) by thelongitudinal velocity. The computation of lateral velocity is affectedby the accuracy of the longitudinal velocity, the errors in thelongitudinal velocity itself will be directly transferred to the errorsin sideslip angle computation.

There exist many methods pursued by the existing stability controls,none of them achieves the accuracy and robustness that is deemednecessary for the ISCS function requirement. For example, in a drivingscenario for a RWD vehicle equipped with the RSC system, during atwo-wheel-lift event (two inside wheels are up in the air), the RSCrequests a large brake pressure in the front outside wheel and there issome driving torque applied to the rear wheel. In this case, none of thefour-wheel speed sensor signals provide useful information to specifythe vehicle longitudinal velocity. A natural approach is to integratethe available longitudinal acceleration to obtain an indication of thevehicle speed. However, due to the gravity contamination through vehiclepitch attitude and the lateral motion contamination due to the vehicle'slateral sliding motion, such an integration of the longitudinalacceleration may have significant errors and may further reduce theeffectiveness of the RSC function or introduce potential falseactivations.

Another problem with the existing method is that on ice or snow the fourindividual wheels may all be in abnormal status (none of them is a goodindication of the vehicle speed due to the fact that none of them is inpure rolling), and the longitudinal acceleration is again contaminatedby the side sliding of the vehicle, the existing method generatessignificant errors which will affect the control actions.

Referring now to FIG. 9, the longitudinal velocity estimation isdetermined using a wheel speed block 800 that receives the wheel speedsand provides a scaling factor 802 and wheel compensation 804 therein.The output of the wheels' speed compensations is provided to alongitudinal reference, contact patch velocity monitoring and thelongitudinal slip ratio block 806. The output of the longitudinalvelocity is fed back into the scaling factor block 802 from block 806.Block 806 receives various inputs from sensors and the like. Forexample, the moving reference frame yaw rate, the steering angle, thewheels and powertrain actuation status, the driver braking status, andthe linear sideslip angle at the moving road frame is provided to block806. A longitudinal velocity derivative is determined using thelongitudinal acceleration at the rear axle in the moving road frame, theyaw rate in the moving road frame, the G pitch and R pitch factors, andthe lateral velocity at the rear angle in the moving road frame. Thelongitudinal velocity derivative is determined in block 808 from theprevious four sensors and is provided to block 806 to determine alongitudinal slip ratio in the contact patch velocity monitor. Theoutput of the block 806 is provided to arbitration and filtering block810, which ultimately determines the longitudinal velocity.

Referring now to FIG. 10, the block 800 is illustrated in furtherdetail. Block 800 includes the front left wheel speed-based algorithm820, the front right wheel-based algorithm 822, the rear leftwheel-based algorithm 824, and the rear right wheel-based algorithm 826.A front wheel based algorithm 828 and a rear wheel-based algorithm 830are also provided. Contact patch velocity estimation 832 and a slipratio computation 834 may also be provided. Computations with thesesignals and the wheel actuation status and driver braking status may beprovided in block 806. Block 840 determines whether the wheels aredivergent. In block 842 if the wheels are divergent, the wheel speedsmay be trusted and the longitudinal reference velocity is outputtherefrom. If the wheels are not divergent in block 842, an SSC filtermay be provided. SSC filter combines the longitudinal velocityderivative with an anti-integration drift filter 846 to provide anoutput therefrom. The specifics of the above-mentioned calculations arefurther described below with respect to block 14.

Referring now to FIG. 11, in step 900 the various wheel speed sensorsare determined. In step 902, the other sensor outputs are determined andtranslated into moving road plane.

The rate change of the vehicle longitudinal velocity in the moving roadframe may be calculated from the signals in the moving road frame instep 904 in the following:{dot over (ν)}_(mrfx)=a_(mrfx)+ω_(mrfz)ν_(mrfray) +g sin θ_(mrfy)  (88)where θ_(mrfy) is the pitch angle of the moving road frame with respectto sea level, it is equivalent to the so-called road inclination angleor road slope. θ_(mrfy) may be calculated in the followingθ_(mrfy)=θ_(sy)−Δθ_(y)−θ_(yr)  (89)where θsy is the global pitch angle of the sensor frame calculated basedon the IMU sensor signals, Δθ_(y) is the sensor pitch misalignment andθ_(yr) is the relative pitch that reflects the suspension heightdifference between the front and the rear suspensions.

Since computing the longitudinal velocity at the location of the centerof the rear axle is desired, the above computation in (88) will befurther changed todν _(mrfrax)=a_(mrfx) +p _(xsl2ra)(ω_(mrfy) ²+ω_(mrfz)²)+ω_(mrfz)ν_(mrfray) +g sin θ_(mrfy)  (90)where p_(xsl2ra) is the longitudinal distance between the sensorlocation and the rear axle and ν_(mrfray) is the lateral velocity at therear axle.

Theoretically, the longitudinal velocity at rear axle ν_(mrfrax) isready to be obtained from (90) through integration. However, due tosensor errors reflected in a_(mrfx), ω_(mrfy) and ω_(mrfz), and thecomputational errors reflected in ν_(mrfray) and θ_(mrfy), such a directlong-term integration will generate significant errors. Instead ofrelying heavily on the integration of dν_(mrfrax) all the time, thewheel speed sensor signals are used. A method to compute thelongitudinal velocity which combines dν_(mrfrax) and wheel speeds isdetermined below.

In step 906, the wheel speeds may be used to determine the longitudinalvelocity. When the wheel speed sensor signals are properly compensatedwith the correct scaling factors, and when the vehicle is under normaldriving conditions, the compensated wheel speed sensor signals are thecorrect indications of the vehicle longitudinal velocity. In suchdriving cases, the wheels are usually operating in a stable condition,i.e., their motion is close to the free rolling. In other drivingsituations, when the wheels are far away from free rolling, wheel speedsare no longer the good indications of the vehicle longitudinal speeds.Such cases could happen when the wheels are braked due to a driver'sbraking request: the wheels are braked due to brake control requests,the wheels are driven with large driving torques (for driving wheels,which usually causes wheels' spinning), the wheels lose traction(driving torque applied to wheels are greater than the road tractionlimit), the wheels slide longitudinally, the wheels slide laterally(vehicle builds up large sideslip angle), or the wheels are up in theair (for example, the inside wheels during a sharp turn).

However if there exists at least one wheel in free rolling motion andthe rest of wheels are in unstable conditions, the wheel speed may stillbe used for determining the vehicle longitudinal velocity.

If the front left wheel is in free rolling or close to free rolling, thevehicle longitudinal velocity at the middle point of the rear axle butprojected on the moving road frame may be calculated based on thiswheel's compensated wheel speed signal as in the following

$\begin{matrix}{{v(0)} = \frac{{\kappa_{0}w_{0}} + {\omega_{mrfz}\left\lbrack {{t_{f}{\cos(\delta)}} - {b\;{\sin(\delta)}}} \right\rbrack}}{{\cos(\delta)} + {{\sin(\beta)}{\sin(\delta)}}}} & (91)\end{matrix}$where δ is the wheel's steering angle (road wheel steering angle), β isthe sideslip angle at the rear axle, b is the vehicle base, t_(f) is thehalf track of the front axle; ω_(mrfz) is the vehicle body's yaw rateprojected in the moving road frame, κ₀ is the wheel speed scaling factorof the front left wheel.

Similarly, if the front right wheel is in free rolling or close to freerolling, the vehicle longitudinal velocity at the middle point of therear axle but projected in the moving road frame may be calculated basedon this wheel's compensated wheel speed signals as in the following

$\begin{matrix}{{v(1)} = \frac{{\kappa_{1}w_{1}} + {\omega_{mrfz}\left\lbrack {{t_{f}{\cos(\delta)}} - {b\;{\sin(\delta)}}} \right\rbrack}}{{\cos(\delta)} + {{\sin(\beta)}{\sin(\delta)}}}} & (92)\end{matrix}$where κ₁ is the wheel speed scaling factor of the front right wheel.

If the rear left wheel is in free rolling, the vehicle longitudinalvelocity at the middle point of the rear axle but projected in themoving road frame may be calculated based on this wheel's compensatedwheel speed signals as in the followingν(2)=κ₂ω₂+ω_(mrfz) t _(r)  (93)where t_(r) is the half track of the rear axle, κ₂ is the wheel speedscaling factor of the rear left wheel. If the rear left wheel is in freerolling, the vehicle longitudinal velocity at the middle point of therear axle but projected in the moving road frame may be calculated basedon this wheel's compensated wheel speed signals as in the followingν(3)=κ₃ω₃−ω_(mrfz) t _(r)  (94)where κ₃ is the wheel speed scaling factor of the rear right wheel.

Based on the above four computed longitudinal velocities from the fourwheel speed sensor signals, the velocity variables with their relativepositions among the four variables may be computed as in the followingν_(fmin)=min(ν(0), ν(1)); ν_(fav)=(ν(0)+ν(1))/2; ν_(fmax)=max(ν(0),ν(1));ν_(rmin)=min(ν(2), ν(3)); ν_(rav)=(ν(2)+ν(3))/2; ν_(rmax)=max(ν(2),ν(3));ν_(min)=min(ν_(fmin),ν_(rmin)); ν_(max)=max(ν_(fmax),ν_(rmax));ν_(mid)=ν_(fav)+ν_(rav)−(ν_(min)+ν_(max))/2;  (95)

For a given vehicle longitudinal velocity ν_(mrfrax), the linearvelocity at each of the wheels but projected along the wheellongitudinal directions in step 908 can be computed asν_(νmrfrax)(0)=ν_(mrfrax) cos(δ)+ω_(mrfz)(b sin(δ)+t _(f) cos(δ))ν_(νmrfrax)(1)=ν_(mrfrax) cos(δ)+ω_(mrfz)(b sin(δ)−t _(f) cos(δ))ν_(νmrfrax)(2)=ν_(mrfrax)+ω_(mrfz) t _(r)ν_(νmrfrax)(3)=ν_(mrfrax)−ω_(mrfz) t _(r)  (96)

Based on those linear corner speeds, the longitudinal slip ratios andtheir related quantities can be calculated in step 910 as in thefollowing, where it is evident ρ(i) is the traditional definition of thelongitudinal slip ratio of the ith wheel

for(i = 0; i < 4; i++) (97)$\left\{ \mspace{25mu}{{{\rho(i)} = {\frac{v(i)}{\max\left( {v_{\min},{v_{vmrfrax}(i)}} \right)} - 1}};} \right.$ρ(i) = min(1, max(−1, ρ(i));${{{d\;{\rho(i)}} = {{p_{dlpf}d\;{\rho(i)}} + {\left( {1 - p_{dlpf}} \right)\frac{{\rho(i)} - {\rho_{z1}(i)}}{\Delta T}}}};}\mspace{275mu}$ρ_(z1)(i) = ρ(i); ρ_(p)(i) = ρ(i)dρ(i); ρ_(r)(i) = v_(vmrfrax)(i)dρ(i); }

Now the quality of the wheel speed signals on which the vehiclelongitudinal velocity can be calculated in step 912 is determined foreach wheel as in the following

Also notice that the braking action at each of the wheels will affectusing that wheel's wheel speed sensor to compute the longitudinalvelocity. For this reason, the ith wheel's slip trend (divergent orconvergent longitudinal slip indicated through the Boolean variableS[i].convergent_slip), acceleration trend (decelerated or acceleratedwheel, indicated through the Boolean variable S[i].whldec andS[i].whlacc) and braking action (indicated through the Boolean variableS[i].inbraking) may be determined in the following

for(i = 0; i < 4; i++) { if (ρ_(p)(i) ≦ 0 ) S[i].convergent_slip = 1; else S[i].convergent_slip = 0;  if ( ρ_(r)(i) > p_(min wacc))S[i].whlacc = 1;  else if (ρ_(r)(i) < − p_(min wacc)) S[i].whldec = 1; else (98)  {  S[i].whlacc = 0; S[i].whldec = 0;  }  if (S[i].ABS = 0 &&S[i].BTCS = 0 & & S[i].YSC = 0   & & S[i].RSC =0 &&S[i].LSC = 0 & &P(i) ≦ p_(minpres))   S[i].inbraking = 0;  else S[i].inbraking = 1;  }where S[i].ABS, S[i].BTCS, S[i].YSC, S[i].RSC and S[i].LSC are Booleanvariables whose active values mean there are ABS, BTCS (brake tractioncontrol), YSC, RSC and LSC brake activations respectively.

The contact patch velocity difference between the left and right wheelsat the same axles and the average of the contact patch velocities at thesame axles can be computed as in the following

$\begin{matrix}{{{{\Delta\; v_{cpfa}} = {{\frac{w_{1} - w_{0}}{2} - {\omega_{mrfz}t_{f}{\cos(\delta)}}}}};}{{v_{cpfa} = {{\frac{w_{1} + w_{0}}{2} - {\omega_{mrfz}b\;\sin\;(\delta)} - {v_{mrfrax}\left( {{\cos(\delta)} + {{\sin(\delta)}\beta_{mrfra}}} \right)}}}};}{{{\Delta\; v_{cpra}} = {{\frac{w_{3} - w_{2}}{2} - {\omega_{mrfz}t_{r}}}}};}{{v_{cpra} = {{\frac{w_{3} + w_{2}}{2} - v_{mrfrax}}}};}} & (99)\end{matrix}$and they can be used to determine if the contact patches are drasticallydifferent from each other at the same axle. Such a logic is conducted asin the following

$\begin{matrix}{\left. {{{if}\left( {{\Delta\; v_{cpfa}} \leq {p_{dfth}v_{mrffavx}}} \right)}\&\&{v_{cpfa} \leq {p_{mfth}v_{mrffavx}}}} \right)\left\{ {{{{S\lbrack 0\rbrack} \cdot {convergent\_ cpv}} = 1};{{{S\lbrack 1\rbrack} \cdot {convergent\_ cpv}} = 1};} \right\}{else}\left\{ {{{{S\lbrack 0\rbrack} \cdot {convergent\_ cpv}} = 0};{{{S\lbrack 1\rbrack} \cdot {convergent\_ cpv}} = 0};} \right\}{{if}\left( {{{\Delta\; v_{cpra}} \leq {p_{dfth}v_{mrfravx}}}\&\&{v_{cpra} \leq {p_{mfth}v_{mrfravx}}}} \right)}\left\{ {{{{S\lbrack 2\rbrack} \cdot {convergent\_ cpv}} = 1};{{{S\lbrack 3\rbrack} \cdot {convergent\_ cpv}} = 1};} \right\}{else}\left\{ {{{{S\lbrack 2\rbrack} \cdot {convergent\_ cpv}} = 0};{{{S\lbrack 3\rbrack} \cdot {convergent\_ cpv}} = 0};} \right\}} & (100)\end{matrix}$

Next the drive train mode and torques are determined in step 914 basedon the driving torque distribution D_(τ) information

$\begin{matrix}{{{if}\left( {D_{\tau} \leq 0} \right)}\mspace{25mu}{{{tDriveMode} = {REAR}};}{{else}\mspace{14mu}{{if}\left( {{D_{\tau} > 0}\&\&{D_{\tau} < p_{lrgdistribution}}} \right)}}\mspace{31mu}{{{tDriveMode} = {TOD}};}{else}\mspace{31mu}{{{tDriveMode} = {FOUR}};}} & (101)\end{matrix}$where REAR means RWD, TOD means torque-on-demand, and FOUR means 4×4mode. p_(irgdistribution) is a threshold for torque distribution todetermine the drive mode. Notice that a more detailed drivetraindetermination can be used.

The braking torque applied to each of the four wheels can be computedbased on the caliper pressure P(i) at the ith wheelτ_(b)(0)=P(0)*p _(brkTGain0); τ_(b)(1)=P(1)*p _(brkTGain1);τ_(b)(2)=P(2)*p _(brkTGain2); τ_(b)(3)=P(3)*p _(brkTGain3);  (102)where p_(brkTGaini) is the braking torque gain for the ith wheel.

Reference Velocity by Integrating Wheel Speed Based Computation with theAcceleration Based Computation

Based on the driver mode and the computed braking torque, the totaltorque applied to the ith wheel can be calculated. For example, in thefollowing, for RWD and FWD modes, the total wheel end torque can becalculated using the engine torque distributed to the axle,τ_(axletorque)

if (tDriveMode = REAR) { τ_(d)(0) = (−1)*τ_(b)(0); τ_(d)(1) =(−1)*τ_(b)(1);$\left. {{{\tau_{d}(2)} = {\frac{\tau_{axletorque}}{2} - {\tau_{b}(2)}}};{{\tau_{d}(3)} = {\frac{\tau_{axletorque}}{2} - {\tau_{b}(3)}}};}\mspace{31mu} \right\}\mspace{31mu}$(103) if (tDriveMode = FRONT) {${{\tau_{d}(0)} = {\frac{\tau_{axletorque}}{2} - {\tau_{b}(0)}}};{{\tau_{d}(1)} = {\frac{\tau_{axletorque}}{2} - {\tau_{b}(1)}}};$τ_(d)(2) = (−1)*τ_(b)(2); τ_(d)(3) = (−1)*τ_(b)(3);  }

In step 916, the reference longitudinal velocity is used to find the lowfrequency portion of the vehicle longitudinal velocities in thefollowing.

Non-wheel lifting case which is indicated by relative roll, wheeldeparture angle and the front wheel control bits

f (| θ_(xr) |≦ p_(75th)p_(roligradient) & & (θ_(wda) = 0) & & S[0].RSC =0 & &S[1].RSC = 0 ) { (104)  if (tDriveMode = REAR)  {

Considering the torque-on-demand drivetrain TOD is a transitional mode,a 4×2 assumption for TOD may be used. For some other powertrains, TODmay not be a transitional mode.

For the four-wheel-coasting-case, the reference longitudinal velocity isramping to the maximum longitudinal velocity ν_(max)

f (  S[0].inbraking = 0 & &S[1].inbraking = 0 & &S[2].inbraking = 0 &&S[3].inbraking = 0 & &Θ_(throttle) ≦ 0 & &τ_(axletorque) ≦p_(maxcoasttorq) ) (105)$\left\{ {{v_{mrfraxref} = {v_{\max} + \frac{\left( {v_{mrfraxref} - v_{\max}} \right)}{\xi}}};} \right\}$where Θ_(throttle) is the throttle angle, ξ is a constant greater than 1which is related to the ramping rate, p_(maxcoasttorq) is a thresholdwhich is the maximum allowed torque for the vehicle to be coasted.

If the above four-wheel-coasting-conditions are not satisfied, thefollowing two-front-wheel-coasting case is performed (one or two rearwheels in braking, or rear wheels in driving):

else if (S[0].inbraking = 0 & &S[1].inbraking = 0) (106) { if(S[0].within_smallband = 1)${v_{mrfraxref} = {{v(0)} + \frac{\left( {v_{mrfraxref} - {v(0)}} \right)}{\xi}}};$else if (S[1].within_smallband = 1)${v_{mrfraxref} = {{v(1)} + \frac{\left( {v_{mrfraxref} - {v(1)}} \right)}{\xi}}};$else if (Θ_(throttle) ≦ 0 & &τ_(axletorque) ≦ p_(maxtorquecost)) { if(v_(f max) > p_(minvel))${v_{mrfraxref} = {v_{f\mspace{11mu}\max} + \frac{\left( {v_{mrfraxref} - v_{f\mspace{11mu}\max}} \right)}{\xi}}};$else v_(mrfraxref) += dv_(mrfrax)ΔT;  } else if ( Θ_(throttle) > 0 ∥τ_(axletorque) > p_(maxtorquecost))$\left. \left. {{v_{mrfraxref} = {v_{fo} + \frac{\left( {v_{mrfraxref} - v_{fo}} \right)}{\xi}}};}\mspace{31mu} \right\}\mspace{31mu} \right\}$

If the four-wheel-coasting-condition and the two wheel-coastingconditions are not satisfied, the two-rear-wheel coasting case ischecked (one or two front wheels in braking):

else if (S[2].inbraking = 0 & &S[3].inbraking = 0 (107) &&Θ_(throttle) > 0 && τ_(axletorque) > p_(maxtorquecost)) { if(S[2].within_smallband = 1)${v_{mrfraxref} = {{v(2)} + \frac{\left( {v_{mrfraxref} - {v(2)}} \right)}{\xi}}};$else if (S[3].within_smallband = 1)${v_{mrfraxref} = {{v(3)} + \frac{\left( {v_{mrfraxref} - {v(3)}} \right)}{\xi}}};$else if (S[0].inbraking = 1 & &S[1].inbraking = 1) { if (v_(f max) >p_(minvel) & & |ρ(i_(ro))|≦ p_(slipratiobd))${v_{mrfraxref} = {v_{r\mspace{11mu}\max} + \frac{\left( {v_{mrfraxref} - v_{r\mspace{11mu}\max}} \right)}{\xi}}};$else v_(mrfraxref) += dv_(mrfrax)ΔT;  }$\left. {{{{else}\mspace{14mu} v_{mrfraxref}} = {v_{rav} + \frac{\left( {v_{mrfraxref} - v_{rav}} \right)}{\xi}}};}\mspace{31mu} \right\}$

If the above four-wheel-coasting and two-wheel-coasting conditions arenot satisfied, the single wheel coasting case for the front-left wheelis checked:

else if (S[0].within_middle = 1&&S[0].convergent_slip = 1&&S[0].convergent_cpv = 1&&S[0].inbraking = 0 &&N(0) > p_(fstatical)(1 −p_(nlloss))) (108)$\left\{ \mspace{20mu}{{v_{mrfraxref} = {{v(0)} + \frac{\left( {v_{mrfraxref} - {v(0)}} \right)}{\xi}}};}\mspace{31mu} \right\}$

If the four-wheel-coasting, two-wheel-coasting and front-leftsingle-wheel-coasting conditions are all not satisfied, the front rightwheel coasting condition is checked:

else if (S[1].within_middle = 1&&S[1].convergent_slip = 1&&S[1].convergent_cpv = 1&&S[1].inbraking = 0 &&N(1) > p_(fstatical)(1 −p_(nlloss))) (109)$\left\{ \mspace{14mu}{{v_{mrfraxref} = {{v(1)} + \frac{\left( {v_{mrfraxref} - {v(1)}} \right)}{\xi}}};}\mspace{20mu} \right\}$

If all the above checked conditions are not satisfied, the rear-rightwheel for coasting conditions is then checked:

else if (S[2].within_middle = 1&&S[2].convergent_slip = 1&&S[2].convergent_cpv = 1&&S[2].inbraking = 0 &&N(2) > p_(fstatical)(1 −p_(nlloss))&&Θ_(throttle) ≦ 0 (110)  &&τ_(axletorque) >p_(maxtorquecoast)&&|β_(mrfra)|≦ p_(ssamidbd))$\left\{ \mspace{14mu}{{v_{mrfraxref} = {{v(2)} + \frac{\left( {v_{mrfraxref} - {v(2)}} \right)}{\xi}}};}\mspace{20mu} \right\}$

If none of the four-wheel-coasting, two-wheel-coasting, and front-left,front-right and rear-left single wheel coasting conditions aresatisfied, the front right wheel for coasting is then checked:

else if (S[3].within_middle = 1&&S[3].convergent_slip = 1&&S[3].convergent_cpv = 1&&S[3].inbraking = 0 &&N(3) > p_(fstatical)(1 −p_(nlloss))&&Θ_(throttle) ≦ 0 (111) &&τ_(axletorque) >p_(maxtorquecoast)&&|β_(mrfra)|≦ p_(ssamidbd))$\left\{ \mspace{14mu}{{v_{mrfraxref} = {{v(3)} + \frac{\left( {v_{mrfraxref} - {v(3)}} \right)}{\xi}}};}\mspace{20mu} \right\}$}

If the vehicle is not in 4×2 mode (RWD mode as discussed before, FWD canbe similarly considered), but in 4×4 mode (that is, in all-wheel-driveor toque-on-demand or 4-high or 4-low modes), the following check isperformed for a single wheel condition regardless what the other threewheels are doing (could be braking, driving or coasting)

else { if (S[0].within_smallband = 1)${v_{mrfraxref} = {{v(0)} + \frac{v_{mrfraxref} - {v(0)}}{\xi}}};$ elseif (S[1].within_smallband = 1)${{v_{mrfraxref} = {{v(1)} + \frac{v_{mrfraxref} - {v(1)}}{\xi}}};}\mspace{79mu}$else if ( S[2].within_smallband = 1)${v_{mrfraxref} = {{v(2)} + \frac{v_{mrfraxref} - {v(2)}}{\xi}}};$ elseif (S[3].within_smallband = 1)${v_{mrfraxref} = {{v(3)} + \frac{v_{mrfraxref} - {v(3)}}{\xi}}};$

If none of the above single wheel condition is satisfied, the followingconvergent wheel speed case and the four wheel coasting case is used:

else if (|v_(max) − v_(min)|< p_(smlth) |v_(max) + v_(min) |)${v_{mrfraxref} = {v_{mid} + \frac{v_{mrfraxref} - v_{mid}}{\xi}}};$else if (S[0].inbraking = 0&&S[1].inbraking = 0 &&S[2].inbraking =0&&S[3].inbraking = 0 (113) &&(Θ_(throttle) ≦ 0&&τ_(axletorque) ≦p_(maxtorquecoast)))$\left\{ \mspace{20mu}{{v_{mrfraxref} = {{\left( {v_{\max} + v_{\min}} \right)/2} + \frac{v_{mrfraxref} - {\left( {v_{\max} + v_{\min}} \right)/2}}{\xi}}};}\mspace{20mu} \right\}$

When the vehicle is driven with throttle off, the following computationsare conducted:

else if (Θ_(throttle) ≦ 0&&τ_(axletorque) ≦ p_(maxtorquecoast))) { if(S[0].within_smallband = 1)${v_{mrfraxref} = {{v(0)} + \frac{v_{mrfraxref} - {v(0)}}{\xi}}};$ elseif ( S[1].within_smallband = 1)$v_{mrfraxref} = {{v(1)} + \frac{v_{mrfraxref} - {v(1)}}{\xi}}$ else if(S[2].within_smallband = 1)$v_{mrfraxref} = {{v(2)} + \frac{v_{mrfraxref} - {v(2)}}{\xi}}$ else if(S[3].within_smallband = 1)${v_{mrfraxref} = {{v(3)} + \frac{v_{mrfraxref} - {v(3)}}{\xi}}};$ elseif (| v_(max) − v_(min) |< p_(smith) | v_(max) − v_(min) |) )$\begin{matrix}{\mspace{20mu}{{v_{mrfraxref} = {v_{mid} + \frac{v_{mrfraxref} - v_{mid}}{\xi}}};}} \\{{{{{else}\mspace{14mu} v_{mrfraxref}} = {v_{\max} + \frac{v_{mrfraxref} - v_{\max}}{\xi}}};}\;}\end{matrix}\mspace{45mu}$

If there are no braking on any of the wheels, then the following isperformed:

else if (S[0].inbraking = 0&&S[1].inbraking = 0 (115) &&S[2].inbraking =0&&S[3].inbraking = 0 ) { if ( S[0].within_smallband = 1)${v_{mrfraxref} = {{v(0)} + \frac{v_{mrfraxref} - {v(0)}}{\xi}}};$ elseif ( S[1].within_smallband = 1)${v_{mrfraxref} = {{v(1)} + \frac{v_{mrfraxref} - {v(1)}}{\xi}}};$ elseif (S[2].within_smallband = 1)${v_{mrfraxref} = {{v(2)} + \frac{v_{mrfraxref} - {v(2)}}{\xi}}};$ elseif (S[3].within_smallband = 1)${v_{mrfraxref} = {{v(3)} + \frac{v_{mrfraxref} - {v(3)}}{\xi}}};$ elseif (| v_(max) − v_(min) |<| v_(max) + v_(min) | p_(smith))${v_{mrfraxref} = {v_{mid} + \frac{v_{mrfraxref} - v_{mid}}{\xi}}};$$\left. {{{{else}\mspace{20mu} v_{mrfraxref}} = {v_{\min} + \frac{v_{mrfraxref} - v_{mid}}{\xi}}};}\mspace{20mu} \right\}$

If none of the above conditions is satisfied, the integration of thetime derivative of the longitudinal velocity along the moving road frameis conducted:

  else      v_(mrfraxref) + = dv_(mrfrax) * ΔT;   } (116)  } }

For a potential inside wheel/wheel lifting case:

else (117) { if ( Θ_(throttle) ≦ 0&&τ_(axletorque) ≦ p_(maxtorquecoast) &&dv_(mrfraxf) ≦ 0&&dv_(mrfraxf) > −p_(mindeepbrakedvc) &&|ρ(i_(ro))|≦p_(slipratiobd)$\left\{ \mspace{20mu}{{v_{mrfraxref} = {v_{ro} + \frac{v_{mrfraxref} - v_{ro}}{\xi}}};}\mspace{20mu} \right\}$else if ( (τ_(axletorque) ≧ p_(mintorquehmu) || Θ_(throttle) ≧p_(minthrottlehmu)) &&dv_(mrfraxf) > 0&&dv_(mrfraxf) ≦p_(mindeepbrakedvc))${v_{mrfraxref} = {v_{fmax} + \frac{v_{mrfraxref} - v_{fmax}}{\xi}}};$else  v_(mrfraxref) + = dv_(mrfrax) *ΔT; } } }

In step 918, The longitudinal velocity may then be computed based on thereference longitudinal velocity and a washout integration of thederivative of the longitudinal velocity such that the non-smooth switchin the reference longitudinal velocity is

if (v_(xmrf) ≧ p_(smspd)) { if((v_(max) − v_(min)) > p_(smpc)(v_(max) +v_(min))) {//Compute High Frequency Portion of Longitudinal Velocityv_(mrfxdyn) = p_(adid)v_(mrfxdyn) + p_(adin)dv_(mrfrax); //Compute LowFrequency Portion of Longitudinal Velocity v_(mrfxss) =p_(adid)v_(mrfxss) + p_(sscn)v_(mrfraxref); v_(mrfx) = v_(mrfxdyn) +mrfxss; v_(mrfxls) = v_(mrfx); v_(mrfyls) = v_(mrfy); } //ComputeLongitudinal Velocity During Convergent Wheel Speeds  else if ((v_(max)− v_(min)≦ p_(smpc) (v_(max) + v_(min))) $\begin{matrix}\left\{ \mspace{20mu}{{v_{mrfx} = {v_{mid} + \frac{v_{mrfx} - v_{mid}}{\xi}}};} \right. \\{\mspace{31mu}{{v_{mrfxss} = {v_{mrfx} + \frac{v_{mrfxss} - v_{mrfx}}{\xi}}};\mspace{14mu}{v_{mrfxdyn} = {v_{mrfx} - v_{mrfxss}}};}}\end{matrix}\quad$ v_(mrfxls) = v_(mrfx); v_(mrfyls) = v_(mrfy); } (118)}

If during low vehicle speed,

else {  //Compute Longitudinal Velocity During Low Speed Driving   v_(mrfyls) + = dv_(mrfray)ΔT;    dv_(mrfxls) = a_(mrfxaug) +w_(mrfz)v_(mrfyls);    v_(mrfxls) + = dv_(mrfrax)ΔT;    if (v_(mrfxls) <0 & &v_(mrfxls) ≧ −v_(max))     v_(mrfxls) = −v_(max); (119)    if(v_(mrfxls) ≧ p_(smspd))     v_(mrfxls) = p_(smspd);    v_(mrfxdyn) =p_(adid)v_(mrfxdyn) + p_(adin)dv_(mrfxls);    v_(mrfxss) =p_(adid)v_(mrfxss) + p_(sscn)v_(mrfxls);    v_(mrfx) = v_(mrfxdyn) +v_(mrfxss); }

The derivative of the longitudinal velocity based on the computedlongitudinal velocitydν _(mrfx) =p _(dervd1) dν _(mrfx−1) −p _(dervd2) dν _(mrfx−2) +p_(dervn)(ν_(mrfx)−ν_(mrfx−2));dν _(mrfx−2) =dν _(mrfx−1);dν _(mrfx−1) =dν _(mrfx);ν_(mrfx−2)=ν_(mrfx−1);ν_(mrfx−1)=ν_(mrfx)  (120);

The Wheel Speed Sensor Scaling Factor

In step 920, the wheel speeds scaling factors are determined such thatthe products of the scaling factors and the wheel speed sensor outputsprovide the true linear speeds of the wheel centers during the wheels'coasting (free rolling). The final individual scaling factors involveseveral separated scaling factor computations, which include the dynamicscaling factors and several static scaling factors including: theleft-to-right delta scaling factor at front axle; the left-to-rightdelta scaling factor at rear axle; the front-to-rear reference deltascaling factor; the global scaling factors.

The static scaling factors are calculated through several sequentialcomputations.

In the first step, the left-to-right delta scaling factor at front axleor at the rear axle are first identified based on the individuallongitudinal velocities calculated from the individual wheel speedsensor output, to try to balance the left and right wheel speed at thesame axle during normal or costing wheel conditions.

In the second step, the reference wheel at front and the reference wheelat the rear are picked to compute the delta scaling factor, which iscalled the front-to-rear reference delta scaling factor.

In the third step, a reference wheel which does not need to have anyscaling factor adjustment and which is one of the front and rearreference wheels used in step 2. The global scaling factor is calculatedbased on this reference wheel through matching its acceleration with thevehicle's longitudinal acceleration.

In the fourth step, the final static scaling factors are generated basedon the delta scaling factors and the global scaling factors calculatedin step 1 to 3.

In parallel to the static scaling factor determination, the dynamicscaling factors are determined based on the dynamic event.

The linear wheel speeds are used to describe the velocities of thecenters of the wheels along their longitudinal directions. Thisinformation can be used to assess the longitudinal wheel slips used inbrake and traction controls (such as ABS, TCS, RSC and ESC) and used todetermine the longitudinal velocity of the vehicle. Such linear wheelspeeds are translational velocities and cannot be directly measuredunless expensive velocity sensors are used. The wheel speed sensor wasinvented for this purpose, however, it is rather misleading to call theoutput from a wheel speed sensor as the linear wheel speed since thewheel speed sensor really measures the wheels rotational speed and itsoutput is the product of such rotational rate and the nominal rollingradius of the wheel. When the wheel's true rolling radius differs fromthe nominal value, the wheel speed sensor output will not be able toreflect the true vehicle velocity.

During the travel of a vehicle, many error sources contribute to thevariation of the rolling radii and the following lists some of them: lowinflation pressure in the tire of the interested wheel (the lowerpressure, the smaller the rolling radius); uneven static loadingdistribution in the vehicle caused unevenly distributed rolling radii;the spare tire usage (the spare tire usually has a rolling radius whichis about 15% to 17% smaller than the nominal rolling radius); theoff-spec tire usage (customers sometimes use large off-spec tires, whichhave larger rolling radii); lateral load transfer during dynamicmaneuvers such as potential RSC event (the load transfer may generateabout 5% reduction in tire rolling radii for outside wheels during a oneor two wheel lift event).

The above error sources will introduce errors in wheel linear speeddetermination, which further affects the accuracy of both wheel and thevehicle state estimations. For example, one of the important wheelstates is the wheel's longitudinal slip ratio, its determination dependson the linear speed of the wheel and the longitudinal velocity of thevehicle. An erroneous computation in the wheel and vehicle states willultimately cause false activations in controls or undermine theeffectiveness of the control functions. Therefore it is desirable tocounteract to the afore-mentioned error sources by adaptively adjustingthe wheel scaling factors, which are the ratios between the true wheelrolling radii and the nominal wheel rolling radii, so as to adaptivelycalibrate the wheel speeds.

By using the nominal rolling radius, the wheel speed sensor outputs canbe expressed asw _(i)=ω_(is) R _(i)  (121)for i=0, 1, 2, 3 (indicating front-left, front-right, rear-left andrear-right wheels), where ω_(i) is the well-known (but misleading) wheelspeed sensor output for the ith wheel which depends on its rollingradius; ω_(is) is the rotational velocity of the ith wheel which isindependent of its rolling radius; R_(i) is the nominal rolling radiusof the ith wheel. Usually the front two wheels and the rear two wheelshave the similar rolling radiiR₀=R₁=R_(f)R₂=R₃=R_(r)  (122)

If the true rolling radius of the ith wheel is denoted as r_(i), thenthe ith wheel speed scaling factor is defined as

$\begin{matrix}{\chi_{i} = \frac{r_{i}}{R_{i}}} & (123)\end{matrix}$

Due to the computational advantage, instead of using (123), the deltascaling factors are used. The left-to-right delta scaling factors forthe front wheels (Δχ_(f)) and rear wheels (Δχ_(r)) are defined as

$\begin{matrix}{{{\Delta\;\chi_{f}} = \frac{r_{0} - r_{1}}{R_{f}}}{{\Delta\;\chi_{r}} = \frac{r_{2} - r_{3}}{R_{r}}}} & (124)\end{matrix}$

The front-to-rear delta scaling factor is defined as

$\begin{matrix}{{\Delta\;\chi_{f\; 2r}} = \frac{2\left( {r_{ireff} - r_{irefr}} \right)}{R_{f} + R_{r}}} & (125)\end{matrix}$where ireff is one of the front wheels which is called the frontreference wheel, whose rolling radius does not need to be adjusted;irefr is one of the rear wheels which is called the rear referencewheel, whose rolling radius does not need to be adjusted.

The wheel scaling factor defined in (123) can also be determined thoughlongitudinal acceleration alignment as in the following

$\begin{matrix}{\kappa_{g} = {{\frac{{\overset{.}{v}}_{x - {MRF}}}{{\overset{.}{v}}_{i}}\mspace{14mu}{if}\mspace{14mu}{\overset{.}{v}}_{i}} \neq 0}} & (126)\end{matrix}$where {dot over (ν)}_(x-MRF) is the time derivative of the longitudinalvelocity obtained from the acceleration sensor signals and thecalculated vehicle attitudes. Notice that {dot over (ν)}_(x-MRF) isprojected on the same plane on which the wheel travels. {dot over(ν)}_(i) is the time derivative of the longitudinal velocity from theith wheel speed sensor (but the turn effect, or say the difference dueto vehicle turning is compensated).

Since the rolling radii are not known prior to the computation,(123)-(125) are not useful for the scaling factor computations. By usingthe sensed wheel angular velocities (wheel speed sensor outputs) and thelongitudinal velocity at the center of the wheels, the rolling radii in(123)-(125) can be further expressed as

$\begin{matrix}{{{r_{0} = {\frac{v_{{wc}\; 0}}{w_{0}}R_{f}}};{r_{1} = {\frac{v_{{wc}\; 1}}{w_{1}}R_{f}}}}{{r_{2} = {\frac{v_{{wc}\; 2}}{w_{2}}R_{r}}};{r_{3} = {\frac{v_{{wc}\; 3}}{w_{3}}R_{r}}}}} & (127)\end{matrix}$where ν_(wci) is the linear longitudinal velocity of the center of theith wheel. Therefore (124) can be expressed as

$\begin{matrix}{{{\Delta\;\chi_{f}} = {\frac{v_{{wc}\; 0}}{w_{0}} - \frac{v_{{wc}\; 1}}{w_{1}}}}{{\Delta\;\chi_{r}} = {\frac{v_{{wc}\; 2}}{w_{2}} - \frac{v_{{wc}\; 3}}{w_{3}}}}} & (128)\end{matrix}$

(128) is still not particularly useful due to the fact that ν_(wci) areunknowns. Considering if the vehicle is driven on a straight road,ideally all ν_(wci)s will be the same, hence if the following relativecomputations are introduced

$\begin{matrix}{{{\Delta\;\kappa_{f}} = \frac{r_{0} - r_{1}}{\left( {r_{0} + r_{1}} \right)/2}}{{\Delta\;\kappa_{r}} = \frac{r_{2} - r_{3}}{\left( {r_{2} + r_{3}} \right)/2}}{{\Delta\;\kappa_{f\; 2r}} = \frac{\left( {r_{i} - r_{j}} \right)}{\left( {r_{i} + r_{j}} \right)/2}}} & (129)\end{matrix}$

The unknowns ν_(wci)s could be eliminated to obtain the followingcomputations which only depend on the known variables

$\begin{matrix}{{{\Delta\;\kappa_{f}} = \frac{w_{1} - w_{0}}{\left( {w_{1} + w_{0}} \right)/2}}{{\Delta\;\kappa_{r}} = \frac{w_{3} - w_{2}}{\left( {w_{3} + w_{2}} \right)/2}}{{\Delta\;\kappa_{f\; 2r}} = \frac{\left( {w_{ireff} - w_{irefr}} \right)}{\left( {w_{ireff} + w_{irefr}} \right)/2}}} & (130)\end{matrix}$

Notice there are two issues associated with (130). The first issue isthe contamination of the vehicle turning effect. That is, when a vehicleis driven in a turn, the outside wheels travel more distances in orderto catch up with the inside wheels and they speed up, which would lookmuch the same as the outside wheels have smaller rolling radii. However,if the corner wheel speed sensor outputs is transferred to the samelocation, this turning effect can be eliminated. The second issue isthat (130) is clearly the determination of the relative scaling factorswith respect to the average wheel speed of the right and the left wheelsfor Δκ_(f) and Δκ_(r), and with respect to the average wheel speed ofthe front and rear reference wheels for Δκ_(f2r).

The scaling factor difference of one wheel with respect to the other isimportant. A better definition for the front delta scaling factor wouldbe

$\begin{matrix}{{\Delta\;\kappa_{f}} = \frac{w_{1} - w_{0}}{\max\left( {w_{1},w_{0}} \right)}} & (131)\end{matrix}$

However due to the later least computation method, if the noises inwheel speeds cause different wheels picked for the max, the above maynot be robust. Instead of using (131), a correction to the computation(130) is conducted as in the following

$\begin{matrix}{{{{\Delta\;\kappa_{f}^{\prime}} = \frac{w_{1} - w_{0}}{\left( {w_{1} + w_{0}} \right)/2}},{{\Delta\;\kappa_{f}} = \frac{\Delta\;\kappa_{f}^{\prime}}{1 - {{{\Delta\;\kappa_{f}^{\prime}}}/2}}}}{{{\Delta\;\kappa_{r}^{\prime}} = \frac{w_{3} - w_{2}}{\left( {w_{3} + w_{2}} \right)/2}},{{\Delta\;\kappa_{r}} = \frac{\Delta\;\kappa_{r}^{\prime}}{1 - {{{\Delta\;\kappa_{r}^{\prime}}}/2}}}}{{{\Delta\;\kappa_{f\; 2r}^{\prime}} = \frac{\left( {w_{j} - w_{i}} \right)}{\left( {w_{j} + w_{i}} \right)/2}},{{\Delta\;\kappa_{f\; 2r}} = \frac{\Delta\;\kappa_{f\; 2r}^{\prime}}{1 - {{{\Delta\;\kappa_{f\; 2r}^{\prime}}}/2}}}}} & (132)\end{matrix}$

Overcoming the first issue by restricting the computation straight linedriving not only limits the screening conditions for the computationsbut could also causes robustness issues, since a true straight linedriving is hard to be determined. In order to solve the first issue,using the wheel speeds with removed turning effects is considered bycompensating the yaw rate sensor signals. That is, the individuallongitudinal velocities are worked with, which are calculated bytransferring the wheel speed signals to the same location. In order toovercome the second issue, the acceleration calibration as in (136) willbe used to compute portion of the scaling factor which could not bedetermined through Δκ_(f), Δκ_(r) and Δκ_(f2r).

An individual longitudinal velocity is defined as the one which measuresthe vehicle longitudinal velocity at the rear axle location which iscalculated by transferring the four individual wheel speed sensorsignals to same rear axle location. The following provides a computationof the individual longitudinal velocities

$\begin{matrix}{{v_{0} = \frac{w_{0} + {\omega_{mrfz}\left\lbrack {{t_{f}{\cos(\delta)}} - {b\;{\sin(\delta)}}} \right\rbrack}}{{\cos(\delta)} + {{\sin(\beta)}{\sin(\delta)}}}}{v_{1} = \frac{w_{1} - {\omega_{mrfz}\left\lbrack {{t_{f}{\cos(\delta)}} - {b\;{\sin(\delta)}}} \right\rbrack}}{{\cos(\delta)} + {{\sin(\beta)}{\sin(\delta)}}}}{v_{2} = {w_{2} + {ct}_{r}}}{v_{3} = {w_{3} - {\omega_{mrfz}t_{r}}}}} & (133)\end{matrix}$where t_(f) and t_(r) are the half tracks for the front and rear axles,b is the vehicle base, ω_(mrfz) is the vehicle's yaw rate projected onthe axle which is perpendicular to the plane on which the wheels aretraveling, which is called moving road frame.

Based on the above individual longitudinal velocities, compute the deltascaling factors may be approximately computed as in the following

$\begin{matrix}{{{{\Delta\;\kappa_{f}^{\prime}} = \frac{v_{0} - v_{1}}{\left( {v_{0} + v_{1}} \right)/2}},{{\Delta\;\kappa_{f}} = \frac{\Delta\;\kappa_{f}^{\prime}}{1 - {{{\Delta\;\kappa_{f}^{\prime}}}/2}}}}{{{\Delta\;\kappa_{r}^{\prime}} = \frac{v_{2} - v_{3}}{\left( {v_{2} + v_{3}} \right)/2}},{{\Delta\;\kappa_{r}} = \frac{\Delta\;\kappa_{r}^{\prime}}{1 - {{{\Delta\;\kappa_{r}^{\prime}}}/2}}}}} & (134)\end{matrix}$

Using the computations from (134) to adjust the wheel speeds leads tothe followingw_(i) ^(comp)=(1−|Δκ_(f)|)ω_(i)w_(j) ^(comp)=(1−|Δκ_(r)|)ω_(j)  (135)

After adjustment in (135) is done, the compensated wheel speeds in step922 will generate the same individual wheel longitudinal velocities inthe front two wheels, or the same individual wheel longitudinalvelocities in the rear two wheels.

Notice that the balanced individual longitudinal velocities could stillbe different from the true values due to the relative feature of thecomputation method in (134). Hence there is a need to do furthercompensation so as to balance the front and the rear individuallongitudinal velocities.

Let ireff be a front reference wheel which is a wheel used as areference to balance the front two wheels, and irefr be a rear referencewheel, which is used as a reference to balance the rear two wheels, then

$\begin{matrix}{{{\Delta\;\kappa_{f\; 2r}^{\prime}} = {2\frac{v_{ireff} - v_{irefr}}{v_{ireff} + v_{irefr}}}}{{\Delta\;\kappa_{f\; 2r}} = \frac{\Delta\;\kappa_{f\; 2r}^{\prime}}{1 - {{{\Delta\;\kappa_{f\; 2r}^{\prime}}}/2}}}} & (136)\end{matrix}$

Due to the noise and disturbance in the wheel speed sensor output, noneof the computations in (134) and (136) have practical significance. Inorder to removing such noises and disturbances factors, a least squareparameter identification method is used here. The least square parameteridentification method is an averaging method which tries to find theoptimal parameters to fit certain amount of data point. The least squarealgorithm for computing Δκ_(f) in (134) can be expressed as in thefollowing

if (front wheel screening condition holds) (137) { n_(f) = n_(f) + 1;if(n_(f) < p_(totlsstesps)) { A_(f) = A_(f) + (v₀ + v₁)²/4;   B_(f) =B_(f) + (v₀ ² − v₁ ²)/2; } else $\begin{matrix}\left\{ \mspace{20mu}{{{\Delta\kappa}_{f} = {\max\left( {{- p_{deviation}},{\min\left( {p_{deviation},\frac{B_{f}}{A_{f}}} \right)}} \right)}};} \right. \\{\mspace{31mu}{{{\Delta\kappa}_{f}^{\prime} = \frac{{\Delta\kappa}_{f}^{\prime}}{1 - {{{\Delta\kappa}_{f}^{\prime}}/2}}};}}\end{matrix}\quad$ A_(f) = 0; B_(f) = 0; N_(f) = 0; Δκ_(f) =p_(dlpf)Δκ_(f) + (1 − p_(dlpf))Δκ′_(f); } }

The least square algorithm for computing Δκ_(r) in (134) can beexpressed as in the following

if (rear wheel screening condition holds) (138) { n_(f) = n_(r) + 1;if(n_(r) < p_(totlsstesps)) { A_(r) = A_(r) + (v₂ + v₃)²/4;   B_(r) =B_(r) + (v₂ ² − v₃ ²)/2; } else $\begin{matrix}\left\{ \mspace{20mu}{{{\Delta\kappa}_{r} = {\max\left( {{- p_{deviation}},{\min\left( {p_{deviation},\frac{B_{r}}{A_{r}}} \right)}} \right)}};} \right. \\{\mspace{31mu}{{{\Delta\kappa}_{r}^{\prime} = \frac{{\Delta\kappa}_{r}^{\prime}}{1 - {{{\Delta\kappa}_{r}^{\prime}}/2}}};}}\end{matrix}\quad$ A_(r) = 0; B_(r) = 0; N_(r) = 0; Δκ_(r) =_(dlpf)Δκ_(r) + (1 − p_(dlpf))Δκ′_(r); } }

Using the delta scaling factors calculated in (137) and (148), theindividual scaling factors of the four wheels could be assigned as inthe following if only the smaller wheel is considered

if (Δk_(f) ≧ 0 and Δk_(r) ≧ 0 ) {  k₁₀ = 1 − Δk_(f);k₁₁ = 1;   k₁₂ = 1 −Δk_(r);k₁₃ = 1;   ireff = 1;irefr = 3;  } else if (Δk_(f) ≦ 0 and Δk_(r)≦ 0 ) {  k₁₀ = 1 + Δk_(f);k₁₁ = 1;   k₁₂ = 1;k₁₃ = 1 + Δk_(r);   ireff =0;irefr = 2;  } else if (Δk_(f) ≦ 0 and Δk_(r) ≧ 0 ) {  k₁₀ = 1 +Δk_(f);k₁₁ = 1;   k₁₂ = 1 − Δk_(r);k₁₃ = 1;   ireff = 0;irefr = 3;  }else {  k₁₀ = 1 − Δk_(f);k₁₁ = 1;   k₁₂ = 1;k₁₃ = 1 + Δk_(r); (139)  ireff = 1;irefr = 2;  }

The least square algorithm for computing Δκ_(f2r) in (134) can beexpressed as in the following

if (front and rear reference wheels screening condition holds) { n_(f2r)= n_(f2r) + 1; if (n_(f2r) < p_(totlsstesps)) { A_(f2r) = A_(f2r) +(v_(ireff) + v_(irefr))²/4;   B_(f2r) = B_(f2r) + (v_(ireff) ² −v_(irefr) ²)/2; } else $\begin{matrix}\left\{ \mspace{20mu}{{{\Delta\kappa}_{f2r} = {\max\left( {{- p_{deviation}},{\min\left( {p_{deviation},\frac{B_{f2r}}{A_{f2r}}} \right)}} \right)}};} \right. \\{\mspace{31mu}{{{\Delta\kappa}_{f2r}^{\prime} = \frac{{\Delta\kappa}_{f2r}^{\prime}}{1 - {{{\Delta\kappa}_{f2r}^{\prime}}/2}}};}}\end{matrix}\quad$ A_(f2r) = 0; B_(f2r) = 0; N_(f2r) = 0; Δκ_(f2r) =p_(dlpf)Δκ_(f2r) + (1 − p_(dlpf))Δκ′_(f2r); } (140) }

Using the delta scaling factor calculated in (140), the individualscaling factors of the four wheels due to the mismatch between the frontreference wheel and the rear reference wheel could be assigned as in thefollowing if only the smaller wheel is considered

if (Δk_(f2r) >= 0) {  k₂₀ = 1−Δk_(f2r);k₂₁ = 1−Δk_(f2r);   k₂₂ = 1;k₂₃ =1;   iref = irefr;  } (141) else {  k₂₀ = 1;k₂₁ = 1−Δk_(f2r);   k₂₂ =1+Δk_(f2r);k₂₃ = 1+Δk_(f2r);   iref = ireff;  }

After the adjustment, all the four wheels can have the exact same wheelspeeds in a straight driving, however, they could be different from thetrue wheel rolling radius since the balances are conducted with respectto the reference wheels. The reference wheel is denoted as iref, whichcould be either the front reference wheel ireff or the rear referencewheel irefr.

If the sensor based longitudinal acceleration is {dot over (ν)}_(x-MRF)the following formula{dot over (ν)}_(x-MRF)=a_(x-MRF)+ω_(z-MRF)ν_(y-MRF)−ω_(y-MRF)ν_(z-MRF)+g sin θ_(y-MRF)  (142)and the time derivative of ν_(iref) as {dot over (ν)}_(iref), then (126)can be expressed as in the following

$\begin{matrix}{\kappa_{g} = \frac{\begin{matrix}{a_{x - {MRF}} + {\omega_{z - {MRF}}v_{y - {MRF}}} -} \\{{\omega_{y - {MRF}}v_{z - {MRF}}} + {g\;\sin\;\theta_{y - {MRF}}}}\end{matrix}}{{\overset{.}{v}}_{iref}}} & (143)\end{matrix}$

A conditional least square parameter identification method for (143) canbe expressed as in the following

if (screening condition holds) {  n_(g) = n_(g) + 1;  if (n_(g) <p_(totlsstesps))  {  A_(g) = A_(g) + v² _(x−MRF); (144)    B_(g) =B_(f) + v_(x−MRF)v_(iref);  }  else  {  k_(g) =max(−p_(deviation),min(p_(deviation),B_(g) / A_(g)));    A_(g) = 0;B_(g)= 0;N_(g) = 0;    Δk_(g) = p_(dlpf)Δk_(f) + (1− p_(dlpf))Δk_(g); } }

If Δκ_(g) is available, then the final static scaling factors can becalculated as in the followingκ_(stati)=κ_(1i)κ_(2i)κ_(g), i=0, 1, 2, 3  (145)

During aggressive maneuver, for example in an RSC event, the vehicleloading is heavily biased towards the outside wheels, especially duringone or two wheel lifting cases. In those cases, there are significantnormal loading increases on outside wheels (up to 100% increase indouble wheel lift case). Let the tire vertical stiffness be K_(t), thevehicle total mass be M_(t), the distance of the c.g. of the vehiclewith respect to the front axle be b_(f) and with respect to front axlebe b_(r), wheel base be b, then the vertical compression of the frontand rear wheels for double wheel lift case can be calculated as

$\begin{matrix}{{{\Delta\; r_{f}} = \frac{b_{r}M_{t}g}{{bK}_{t}}}{{\Delta\; r_{r}} = \frac{b_{r}M_{t}g}{{bK}_{t}}}} & (146)\end{matrix}$and in normal driving conditions, they assume the values

$\begin{matrix}{{{\Delta\; r_{f\; 0}} = \frac{b_{r}M_{t}g}{2{bK}_{t}}}{{\Delta\; r_{r\; 0}} = \frac{b_{r}M_{t}g}{2{bK}_{t}}}} & (147)\end{matrix}$

Hence the incremental vertical tire compression changes are thedifference between (146) and (147). If taking some common values such as

$\begin{matrix}{{M_{t} = {2704\mspace{11mu}{kg}}},{K_{t} = {300000\frac{N}{m}}},{b_{f} = {1.451m}},{b_{r} = {1.573m}},{b = {3.024m}},{then}} & (148) \\{{{{\Delta\; r_{f}} - {\Delta\; r_{f\; 0}}} = {\frac{b_{r}M_{t}g}{2{bK}_{t}} = {{0.021m} = {5.57\%\mspace{14mu}{of}\mspace{14mu} R_{f}}}}}{{{\Delta\; r_{r}} - {\Delta\; r_{r\; 0}}} = {\frac{b_{r}M_{t}g}{2{bK}_{t}} = {{0.023m} = {6.10\%\mspace{14mu}{of}\mspace{14mu} R_{r}}}}}} & (149)\end{matrix}$where R_(f)=R_(r)=0.377 m denote the nominal rolling radii of the tires.Hence for double wheel lift case, the outside tires could have around 5%reduction in rolling radius. For this reason, a scaling factor iscomputed to compensate this

if (|θ_(xr) |≦ p_(35th)p_(rollgrad)) {  κ_(dyn0) = 1; κ_(dyn1) = 1;κ_(dyn2) = 1; κ_(dyn3) = 1;  } else {  if (θ_(xr) < 0)$\left\{ \mspace{20mu}{{\kappa_{{dyn}\; 0} = {\max\left( {{1 - p_{deltalatamax}},{1 - {\frac{{\theta_{xr}} - {p_{35{th}}p_{rollgrad}}}{p_{40{th}}p_{rollgrad}}p_{deltalatamax}}}} \right)}};} \right.$(150) κ_(dyn2) = κ_(dyn0); κ_(dyn3) = 1; κ_(dyn3) = 1;   } else$\left\{ \mspace{20mu}{{\kappa_{{dyn}\; 1} = {\max\left( {{1 - p_{deltalatamax}},{1 - {\frac{{\theta_{xr}} - {p_{35{th}}p_{rollgrad}}}{p_{40{th}}p_{rollgrad}}p_{deltalatamax}}}} \right)}};} \right.$κ_(dyn3) = κ_(dyn1); κ_(dyn0) = 1; κ_(dyn2) = 1;    } }where κ_(dyni) (for i=0, 1, 2, 3) denotes the dynamic scaling factor forthe ith wheel.

The final individual scaling factors can be calculated as in thefollowingκ_(i)=κ_(stati)κ_(dyni)=κ_(1i)κ_(2i)κ_(g)κ_(dyni), i=0, 1, 2, 3  (151)

In the following example the above computations can be used forcompensating the wheel speed sensor signals. The front-left wheel andthe rear left wheels are wheels presumed to have smaller rolling radii,then the compensated wheel speeds using the above two stagecompensations can be expressed as in the following for Δκ_(f2r<)0 caseω₀ ^(comp)=(1−|Δκ_(f)|)(1−|Δκ_(f2r)|)ω₀ω₁ ^(comp)=(1−|Δκ_(f2r)|)ω₁ω₂ ^(comp)=(1−|Δκ_(r)|)ω₂ω₃ ^(comp)=ω₃  (152)

and for Δκ_(f2r)≧0 caseω₀ ^(comp)=(1−|Δκ_(f)|)ω₀ω₁ ^(comp)=ω₁ω₂ ^(comp)=(1−|Δκ_(r)|)(1−|Δκ_(f2r)|)ω₂ω₃ ^(comp)=(1−|Δκ_(f2r)|)ω₃  (153)

It can be seen that in either case, there is one wheel which does notneed to be compensated (rear-right wheel for (151) and front right wheelfor (152)). If considering κ_(g) and κ_(dyni), further compensation for(160) may be achieved as in the followingω₀ ^(comp)=κ_(g)(1−|Δκ_(f)|)(1−|Δκ_(f2r)|)κ_(dyn0)ω₀=κ₀ω₀ω₁ ^(comp)=κ_(g)(1−|Δκ_(f2r)|)κ_(dyn1)ω₁=κ₁ω₁ω₂ ^(comp)=κ_(g)(1−|Δκ_(r)|)κ_(dyn2)ω₂=κ₂ω₂ω₃ ^(comp)=κ_(g)κ_(dyn3)ω₃=κ₃ω₃  (154)

or for (153) as in the followingω₀ ^(comp)=κ_(g)(1−|Δκ_(f)|)κ_(dyn0)ω₀=κ₀ω₀ω₁ ^(comp)=κ_(g)κ_(dyn1)ω₁κ₁ω₁ω₂ ^(comp)=κ_(g)(1−|Δκ_(r)|)(1−|Δκ_(f2r)|)κ_(dyn2)ω₂=κ₂ω₂ω₃ ^(comp)=κ_(g)(1−|Δκ_(f2r)|)κ_(dyn3)ω₃=κ₃ω₃  (155)

The detailed algorithm together with the screening conditions used inthe algorithms may be found in the detailed logic section.

Referring now also to FIGS. 12A, 12B, and 12C, one advantage of thepresent invention is illustrated. As mentioned above, the longitudinalvelocity, the lateral velocity determined above may be used to determinethe sideslip of the vehicle. In FIG. 12A, a base vehicle withoutstability control is illustrated, As can be seen, before achievingstability the vehicle may completely slide sideways. In a traditionalstability control system shown in 12B, the vehicle may slide sidewaysand leave the roadway before regaining control. This is becausetraditional stability control may be too late and the vehicle mayovershoot the desired course. Using the present invention illustrated in12C, an advance yaw stability control using precise sideslip informationreacts quicker than standard stability control so that the desiredcourse or lane may be maintained.

The Vehicle Sideslip Angle at the Rear Axle

As mentioned above, the sideslip angle β_(LSC) of the vehicle body andits time derivative are used in LSC. β_(LSC) is the sideslip angleβ_(mrfra) of the vehicle body at its real axle location, measured alongthe moving road frame, measures the lateral stability of a movingvehicle. The aforementioned sideslip angle can be defined as in thefollowing

$\begin{matrix}{\beta_{LSC} = {\tan\left( \frac{\upsilon_{mrfray}}{\upsilon_{mrfrax}} \right)}} & (156)\end{matrix}$

where ν_(mrfrax) and ν_(mrfray) are the longitudinal and lateralvelocities of the vehicle body at its rear axle measured along thex-axis and the y-axis of the moving road frame.

β_(LSC) thus defined can be related to the signals calculated from thesensor measurements such as the lateral acceleration, the yaw rate, thebank and slope angles of the moving road frame and the referencevelocity as in the following:

$\begin{matrix}{{{d\;\beta_{{LSC}\; 2}} = {{\left\lbrack {{- \omega_{mrfz}} + \frac{{a_{mrfyra}\upsilon_{mrfrax}} - {g\;\sin\;\theta_{mrfx}\cos\;\theta_{mrfy}}}{\upsilon_{mrfrax}}} \right\rbrack\left\lbrack {1 + {\cos\left( \beta_{{LSC}\; 2} \right)}} \right\rbrack} - {\frac{{\overset{.}{\upsilon}}_{mrfrax}}{\upsilon_{mrfrax}}{\sin\left( \beta_{{LSC}\; 2} \right)}}}}{\beta_{LSC} = \frac{\beta_{{LSC}\; 2}}{2}}} & (157)\end{matrix}$

Both (156) and (157) can be used to compute β_(LSC). (146) requires thecomputation of the lateral velocity while (157) does not need to have aseparate computation of lateral velocity. In the following equation(157) is used to compute β_(LSC). Due to the inevitable sensoruncertainties in lateral acceleration and yaw rate sensors, and errorsin the computed road bank and slope, a pure integration of (157) wouldgenerate large error.

In step 924 a dynamic sideslip angle may be determined, such a dynamiccomputation calculate the integration of (157) with passing through ahigh-pass-filter. Such integration plus high pass filter is called ananti-integration-drift (AID) filter. Such computation can be done as inthe following

$\begin{matrix}{{\left. {{\beta_{{LSC}\; 2}\left( {k + 1} \right)} = {{d_{1}{\beta_{{LSC}\; 2}(k)}} - {d_{2}{\beta_{{LSC}\; 2}\left( {k - 1} \right)}}}} \right\rbrack + {n_{1}\left\lbrack {{d\;{\beta_{{LSC}\; 2}\left( {k + 1} \right)}} - {d\;{\beta_{{LSC}\; 2}\left( {k - 1} \right)}}} \right\rbrack}}{{\beta_{{LSC}\; 2}(0)} = {{2\;{\beta_{mrflinr}(0)}{\beta_{{LSC} - {DYN}}\left( {k + 1} \right)}} = \frac{\beta_{{LSC}\; 2}\left( {k + 1} \right)}{2}}}} & (158)\end{matrix}$where d₁, d₂ and n₁ are the coefficients of the AID filter.

The computation in (158) captures the dynamic portion of the sideslipangle, which could be accurate during aggressive maneuvers but it couldbe either under-estimated or overestimated in less dynamic but unstablesituations such as driving on a low mu road surface. For this reason,(158) above does not have much use unless a compensation for lessdynamic portion can be calculated. In order to conduct less dynamiccompensation, the similar scheme used in the RSG unit of the ISS may beconducted.

The less-dynamic portion might calculated from the previous computationof ν_(mrfray) and ν_(mrfrax) through the following steady-state-recovery(SSR) filtering

$\begin{matrix}{\left. {{\beta_{{LSC}\; - {SS}}\left( {k + 1} \right)} = {{d_{1}{\beta_{{LSC}\; - {SS}}(k)}} - {d_{2}{\beta_{{LSC}\; - {SS}}\left( {k - 1} \right)}}}} \right\rbrack + {{f_{1}\left\lbrack \frac{\upsilon_{mrfray}}{\upsilon_{mrfrax}} \right\rbrack}\left( {k + 1} \right)} + {{f_{2}\left\lbrack \frac{\upsilon_{mrfray}}{\upsilon_{mrfrax}} \right\rbrack}(k)} + {{f_{3}\left\lbrack \frac{\upsilon_{mrfray}}{\upsilon_{mrfrax}} \right\rbrack}\left( {k - 1} \right)}} & (159)\end{matrix}$with proper filter coefficients f₁, f₂ and f₃.

In step 928 the final sideslip angle may be expressed asβ_(LSC)=β_(LSC-DYN)+β_(LSC-SS)  (160)

Advantageously, the present invention provides an improved sideslipangle determination by fully utilizing the available measured andcalculated signals from the ISS system. Such computation corrects forgravity and nonlinearities as well as steady state sideslip anglefactors and removing low frequency drift due to the inevitableintegration error due to sensor signal uncertainties such as zero-offsetand temperature dependent offset drifting, error in the computedsignals. Most importantly the sideslip angle calculated here is definedin the moving road plane, which reflect the true objective of the LSCand which is different from many existing calculations that are definedalong the body-fixed frame.

In step 930 the vehicle and the various control systems described abovemay then be controlled in response to the final sideslip angle. Asmentioned above, engine, brakes, steering and other actuators may becontrolled to change the dynamics of the vehicle.

While particular embodiments of the invention have been shown anddescribed, numerous variations and alternate embodiments will occur tothose skilled in the art. Accordingly, it is intended that the inventionbe limited only in terms of the appended claims.

1. A method of controlling a vehicle system comprising: measuringvehicle dynamic conditions: determining a desired sideslip angle, anactual sideslip angle, a desired yaw rate and an actual yaw rate in amoving road plane using the measured vehicle dynamic conditions:generating a control signal in response to the desired sideslip angle,the actual sideslip angle, the desired yaw rate and the actual yaw ratein the moving road plane; and controlling a vehicle system in responseto the control signal.
 2. A method as recited in claim 1, furthercomprising: determining a moving road frame lateral acceleration;determining a moving road frame longitudinal acceleration; and whereindetermining an actual sideslip angle further comprises determining theactual sideslip angle in response to the moving road plane lateralacceleration and the moving road plane longitudinal acceleration.
 3. Amethod as recited in claim 2 further comprising determining the movingroad plane lateral acceleration in response to a pitch angle of thevehicle and a roll angle of the vehicle.
 4. A method as recited in claim3 wherein the pitch angle comprises a relative pitch angle and the rollangle comprises a relative roll angle.
 5. A method as recited in claim2, further comprising determining the moving road plane lateralacceleration in response to a pitch angle of the vehicle, a roll angleof the vehicle, a lateral acceleration of the vehicle, a verticalacceleration of the vehicle and a longitudinal acceleration of thevehicle.
 6. A method as recited in claim 1 further comprisingdetermining the moving road plane lateral acceleration of the vehicle inresponse to a lateral acceleration sensor in the body frame.
 7. A methodas recited in claim 1 further comprising determining the moving roadframe longitudinal acceleration of the vehicle in response to alongitudinal acceleration sensor in the body frame.
 8. A method asrecited in claim 1 further comprising determining the moving road planelongitudinal acceleration in response to a pitch angle of the vehicle, aroll angle of the vehicle, a lateral acceleration of the vehicle and avertical acceleration of the vehicle.
 9. A method as recited in claim 8wherein the pitch angle comprises a relative pitch angle and the rollangle comprises a relative roll angle.
 10. A method as recited in claim1 wherein determining an actual yaw rate comprises determining theactual yaw rate in response to a yaw rate signal from a yaw rate sensor,a pitch rate signal from a pitch rate sensor and a roll rate signal froma roll rate sensor.
 11. A method as recited in claim 1 whereincontrolling a vehicle system comprises controlling a stability controlsystem.
 12. A method as recited in claim 1 wherein controlling a vehiclesystem comprises controlling a vehicle braking system.
 13. A method asrecited in claim 1 wherein controlling a vehicle system comprisescontrolling an electronic throttle control.
 14. A method as recited inclaim 1 wherein controlling a vehicle system comprises controlling avehicle braking system and an electronic throttle control.
 15. A methodof controlling a vehicle having a brake and an electronic throttlecomprising: determining a relative roll angle and a relative pitchangle; determining a body-fixed frame longitudinal acceleration, abody-fixed frame lateral acceleration and a body-fixed frame verticalacceleration; transforming the body-fixed frame longitudinalacceleration, body-fixed frame lateral acceleration and body-fixed framevertical acceleration to a moving road plane lateral acceleration, amoving road plane longitudinal acceleration and a moving road planevertical acceleration using the relative roll angle and the relativepitch angle; computing an actual yaw rate and an actual vehicle sideslipangle measured on the moving road plane; computing a desired yaw rateand a desired sideslip angle measured on the moving road plane;computing a difference between the actual sideslip angle and the desiredsideslip angle to form a sideslip error; computing yaw rate errorbetween the actual yaw rate and the desired yaw rate; computing a demandyaw moment based on the sideslip error and yaw rate error; computing atarget wheel longitudinal slip ratio based on the demand yaw moment;controlling the vehicle brakes to conduct slip control based on thetarget wheel longitudinal slip ratio.